Are humans artifacts?
Short answer: No.
Longer Answer:
UPDATED ANSWER FROM THE COMMENTS
To say that you are a creation of your parents, and then go on to describe how a table or a cabinet is created by a designer/maker, would be to change the meaning of 'create' partway through. If I push a snowball off a mountain, it may or may not gather speed and pick up snow to become a cartoonishly huge boulder by the time it reaches the bottom. Regardless of what happens, I haven't 'created' anything in the usual sense, even though I initiated the series of events that led to the formation of the giant snowball. Similar for having sex - kicking off the chain of chemical reactions that results in a new human being, whether by accident or by intent, is categorically different from deliberately making something for a specific purpose.
Also, coming back around to your original definition, artifacts need to meet at least three criteria:
- An artifact is an object
- That has been intentionally made
- For a certain purpose
[1]: Are humans objects? Under normal circumstances, 'object' would refer to something inanimate, so I would say no.[2]: Can a human be intentionally made? Perhaps: While I would say no, this point is the most open to quibbling. However, if any one of these three criteria fail, humans cannot be classed as artifacts, so let's move on. [3]: Can a human be made for a certain purpose? Here I would say no - human beings get to define their purpose, they don't have to accept an imposed purpose. There's a reason we cheer for the Rebellion taking on the Empire, after all.
Since humans fail to meet all criteria by most interpretations, and at minimum fail to meet criteria [3], we are in no danger of being artifacts.
ORIGINAL ANSWER
Your quoted definition and subsequent question hinge on the answer to one specific (unstated) question: Are humans designed? If humans are the products of deliberate design, either humans are artifacts or (if we're sufficiently uncomfortable with that classification) the definition of artifacts needs to be revisited/revised. If humans are not designed, we cannot be artifacts.
Fortunately for our egos, all evidence points to human beings being a current result of evolution, not of design (intelligent or otherwise). Intelligent Design Creationists have put a lot of money and effort into spreading misinformation, and a full takedown of all their claims would be to create an entire website dedicated to cataloging and rebutting ID claims. Such an undertaking is beyond the scope of a stackexchange.com answer, but fortunately others have already taken the time and effort to do most of the work for us already.
With your edit, you add:
What I mean is that out of all animals, only humans (at least normal ones) seem to conceive children with an intention (e.g. with an intention of having another loved one, etc.) and not just because they desperately want to reproduce.
Until technology reaches the point where we can directly guide the reproduction process and make engineer changes or aesthetic improvements, the intent to have a child does not make the child 'designed' and ergo not an artifact. Intent to have a child or not, none of us have any control over the messy, biological processes of genetic recombination and development that leads to the birth of a new human being, but I can see this becoming an issue that could be revisited as technology marches on.