Natural kinds are kinds that correspond to a grouping that reflects the structure of the natural world rather than the interests and actions of human beings.
But for a kind or grouping to exist, the constituents of that grouping must be similar to each other in some way. Goodman showed that similarity is likely a vacuous concept and is context dependent by its very nature. “A is similar to B” or even “A is similar to B with respect to X” can be rephrased as “A and B both are C with respect to X.” This seems to get rid of the term entirely.
Now, given that what attribute of X one chooses to compare between A and B seems context dependent and arbitrary, how can there possibly be any kinds that are independent of human interest/motivation? Lastly, aren’t all abstract objects not directly part of the natural world? So how can there be “natural” kinds anyways?