If you doubt a claim X, should this very state of being in doubt be justified? How does one justify doubt in the first place? One can technically doubt anything except experience. But few would say that doubt in every area is justified. For example, is one justified in doubting that the earth is a sphere? Many would say no.
So if one does doubt that the earth is a sphere, would that mean that he has to somehow justify his doubt? How would this be done?
The word "certainty," which is the English linguistic foil of the word "doubt," also happens to carry with it a sense of specificity, as when we say, "I met a certain cat on a certain road on a certain day." It is no surprise that Descartes would link clarity and certainty, then, since the vagueness of boundaries-by-generalization is then to be contrasted with the goal of identifying sharply demarcated particulars.
Yet then what is doubt, that it should be opposed to the other (though not wholly separate?!) main concept of certainty? A similar, or equivalent, notion is of the suspension of belief or disbelief. We would not often speak of doubting things that we never even thought of before (I do not doubt that the Goddess of Algebra wears a top hat when performing for guests in the Gardens of Planet X), but this still leaves some room for speaking of doubt about assertions that we have yet to agree or disagree with in substance.
So, waiving complications regarding the diversity in negation theory, let us suppose there is (at least) passive doubt = not believing, and also active doubt = believing not. If our minds are not tabula rasae, then there might be cases where we are otherwise in the passive state modulo some beliefs, yet as a result of active suppression of our innate beliefs, then. If we think that every action, even every mental action, is open to the question of justification, then we could have passive doubts that are justifiable (or unjustifiable, as the case may be). On the other hand, a truly innate belief might be one that we are not able to suppress (or only suppress if we physically damage our brains); perhaps such things would be like Wittgenstein's "hinge propositions."
At any rate, it is active doubt in the direct sense that will call for justification by the by. One form of this justification might be coherentism, which at least involves consistency on our part. If one has a high standard of evidence, then, the motive of consistency should lead us to doubt as many claims of a certain class as possible together instead of being a mere "contrarian" and going against "the official line." So someone who is willing to believe that the Earth has a specific shape only if they go out and explore every direction accessible to them (to find a flat edge or to wrap around a curved surface), and who doubts all assertions about said shape until they have done their own explorations, and who resists believing in testimony even when it is inconvenient for them to do so, at least seems more justified in maintaining their state of doubt than the Flat Earther who combines the Bible and the conspiracy-theorist sector of the Internet to form their basis for attributing a lack of curvature to the planet's expanse. (I mean, this seeming can be qualified further by noting that other celestial objects apparently are curved, too, and these are objects visible "as a whole" from our current vantage, so unless we had reason to think that matter formed a square or a cube in the Earth's case and something more rounded in every other case that is visible to us, well...)
But note that many self-styled skeptics are only actively skeptical just so far as is dialectically convenient for them while they play word games with "normies." They will doubt the "official line" when it suits them (witness their propensity to cite official death rate statistics over the last year as "evidence" that COVID vaccines are causing a "depopulation event"). They will excuse this double-minded citation due to cynicism ("When elites and the mainstream media say positive things, don't trust them! But when those folks say bad things, you best believe they mean them...). So even if attempts at universal active doubt are intelligible and also justifiable, it is going to be hard to find concrete examples of when this state of affairs has actually obtained. (Note: these so-called skeptics don't seem to doubt, "There are elites," and, "There is a mainstream media," for example, all that much; I've challenged them on the latter, pointing to the diversity of media companies out there, to be met with a pseudopsychology "proof" that all these media companies can be clumped together as a monolith worthy of the word "the" prefacing them.)
Even Descartes, for instance, seems to have implicitly, or pragmatically, lacked doubt about the existence of the writing materials he must've used to put the Meditations down on paper.
?! It is easier to be certain about specific propositions than generalizations, perhaps; or at least, sometimes this tends to be the case. For a (universal, or at least broad) generalization runs more of a risk of being arrived at by an inductive fallacy, perhaps, than does a more one-off claim ("All (or at least most) ravens are like writing desks," vs., "This one raven that I'm looking at in bad lighting is like a writing desk," say).
Your question is based on the false assumption that it can be answered without considering specifics. It is rather like asking whether objects in France are bigger than objects in Germany- the answer depends on the objects and on what you mean by bigger.
Whether you need to justify a doubt depends on the circumstances. If you are an expert witness in court, doubting the evidence of a witness, you will certainly be expected to justify your doubt. If you doubt you will enjoy a holiday in Skegness, you are free to decide not to visit that delightful resort without having to justify your reservations.
Whether and how you might justify a doubt depends on the nature of the doubt. If you doubt your friend can lift 50kg with one hand, the doubt can be put to the test straightforwardly. If your doubt is about a matter of opinion, then you might not be able to justify it to the complete satisfaction of others.
The general recipe to justify a doubt is to reason logically from relevant evidence to the effect that the matter doubted is inconsistent with what a reasonable person would believe.
We know from experience and observation (if we assume for a moment that our experiences and observations are reliable), that doubt is very often well-justified, in that it leads us to be skeptical of propositions which turn out to be false. This in turn often leads us to progress our knowledge, by fine-tuning it so that it becomes more aligned with reality (at least, perceivable reality).
To use - pedantically perhaps - your example of the Earth as a sphere... doubt about that very claim leads us to research and discover that the Earth is actually an imperfect sphere; an oblate spheroid or ellipsoid.
So, if 'epistemic justification' is described as something like:
When you have epistemic justification for believing a proposition p, you thereby have a knowledge-contributing entitlement or right or warrant or good reason to believe that p is true...
... then our experience to date would suggest it is reasonable to claim that doubt is epistemically justified because:
'P: We have good reason to believe that doubt often contributes to a more accurate understanding of whether or not a claim comports with reality'.
Of course, even this statement is then subject to doubt, but this should cause little problem if it is subsequently investigated, for it should align with with the available evidence.
While I suspect that the Problem of Skepticism is more appealing to the philosophically inclined, it's a perfectly valid question of why shouldn't we just have faith and undermine the importance of doubt in critical thinking. While theology isn't my cup of tea (and you might also pursue an answer from theologians in addition to secular professional philosophers who are overwhelming fallibilists (IEP)), religious epistemologies of fideists in the extreme may reject reason; since faith is a powerful tenet in these believes, it might be that argumentation to for and against doubt may be more developed.
I believe that doubt seems rather intuitive to anyone who professes a modicum of skepticism, and it's easy to see why. Moving from a naive realism even to a direct realism such as the position Searle outlines in his Seeing Things As They Are (GB) requires one to acknowledge certain experiences that underlie the need for justification of knowledge. A short, influential list cited repeatedly in philosophical works is illusion, confabulation, fallacy, hallucination, and falsity such as lying. And to boot, most people have experience with these in one forms or another (particularly if one sees dreams as a form of hallucination). I think these sources that reinforce the notion of doubt are relatively ubiquitous in works like Descartes, Hume, etc. and require little in the way of justification.
I would suggest that certain types of doubt absolutely require epistemic justification, mainly the reliability of conscious experience in determining truth. This can be seen in the canon vaguely as the struggle between rational and empirical philosophers, caricatured as a Descartes vs. Hume. The rationalists starting with Descartes have long held that conscious introspection is a reliable and thorough indicator of what happens between the ears; to see is to believe is a popular adage that moves in this direction of thinking. The philosophical exploration of certainty (IEP) is one activity that probes the opposite of doubt, which might best be conceived as an intuition. Modern cognitive science has shown beyond a shadow of doubt that human cognition is subject to bias and error and subconscious processes that betray any claims of the reliability of the rational, conscious mind, at least as Descartes envisioned it in his Meditations on First Philosophy (GB).
How is it, when things so obvious to the conscious mind, that it can be so wrong? Why should I doubt the banana before me is not yellow? Why should I not believe in a creator when the world seems so complex that a designer seems the only reasonable explanation for things? Why should I give any credence to wave-particle duality when notions of substance and material are so good at explaining the universe? Why wouldn't my memory of what I saw 10 minutes ago be adequate as eyewitness testimony to support the conviction of someone accused of a crime? It is here that the justification of doubt occurs in fifty different ways. Each of those justifications, then, is a philosophical argument to explain why intuitions of certainty may be wrong, and in contemporary philosophy often rely on a naturalized epistemology (IEP) to bring the latest findings of neurology, criminology, or sociology to bear on thinking.
One cent.
Doubting something, is a also a kind of assertion, eg that "this is doubtful".
Refusing to justify an assertion based on something (even on something as simple as something self-evident), means one is accepting that some assertions need no justification at all. But if that is the case, then why ask for (further) justification for the original statement? One then is bound to accept justification is not necessary for (at least some) assertions.
This results in using double standards and asking for special epistemological treatment regarding statements and assertions.
A justified doubt/challenge promotes understanding and leads to better and better arguments for/against some assertion. In other words, it promotes knowledge. An unjustified doubt does not promote knowledge. Paraphrasing a known maxim: "What is claimed without justification, can be dismissed without justification".
On top of that, if reality is such that some assertions are simply given (ie they are foundational) or have been justified to the maximum degree, then the doubter, by asking for (further) justification, without being able to justify the need for that (ie without being able to argue/show the assertion is not foundational or not adequately justified), makes an epistemological error.
PS: The justification for a doubt/challenge, being just another statement/assertion, is not different than justifying any other statement.
