There are two claims that people usually conflate when they make the statement that one should not pursue the impossible. First, there is a positive claim about the impossible, namely, that it cannot be achieved. Second, there is a normative claim that derives from the positive claim, i.e., that because the impossible cannot be done, it ought not to be pursued.
To me, there is no compelling reason why the normative claim must necessarily follow from the positive claim. I have no qualms with the positive statement, since something that is impossible is by definition unattainable. But to be able to make a normative claim about it is to assume that one ought only to act on things that he has a chance of achieving.
That assumption, which connects the positive to the normative, is not logically necessary. When asked, most people would respond by saying that because the impossible cannot be done, one ought not to waste time/resources/effort on it, and should instead use those resources to do something else.
But why is this utilitarian/practical argument logically necessary? There is no compelling necessity that requires one to adhere to this absolutely. In fact, the ultimate, foundational justification for this utilitarian view is utility itself. Hence, this entire claim–that people should not pursue the impossible–is based on many claims and assumptions that are not by themselves self-evident or inherently true.
All I’m suggesting is that questions regarding what is considered “impossible” are by no means settled questions. There are important questions that the individual must wrestle with. It’s not so easy or so obvious as to require no thought period.