Is this a fallacy? What kind?

My friend doesn’t want to check his test scores because he claims that he is apathetic towards them and that ‘an unaimed arrow never misses”. Isn’t it also true that an unaimed arrow always misses?

This might be a horrible life philosophy (IMO), I don't think this is fallacious. It is true that if you have no goal, you cannot fail at the goal. I wouldn't say that this also means they always fail, but I would say that they never succeed at the goal.

No fallacy, but it could be the ostrich effect cognitive bias: {youtube title=} youtu.be/BGbk5099z3o{/you. . .

Let's examine the first claim:

‘an unaimed arrow never misses”. of course, this is more of a riddle than a logical fallacy. It actually sounds more like a zen buddhist flash card akin to
"What is the sound of one hand clapping? It's an appeal to mystery (woo) and not designed to have a logical answer because it is not a logical claim in the first place. Now it could be that the claimant intends it as a criticism like Thomas Gray's Ode on a Distant Prospect of Eton College, "Where ignorance is bliss, 'tis folly to be wise." In other words, it's easy to imagine you're a success if you never try. Which, indeed, has a certain psychological/moral weight to it.

To aim something requires positioning or directing a discharged projectile to hit a target or travel along a specific path. Therefore the non act of not aiming could be construed as either doing nothing or firing randomly. If you don't aim or fire at a target, it is virtually impossible or, at least high unlikely you will hit any target. Since there is no target to aim at the claim contradicts itself.

Likewise the response "Isn’t it also true that an unaimed arrow always misses?' is actually just as false because it asks, isn't it also true? No, neither claim is true. Also, and arguably, there are instances in physics, such as The Large Hadron Collider (LHC) in CERN, where random firings do indeed hit their target.

FYI, Daniel Dennett offers a very funny lecture on similar types of distractions and deceptions of theological "spin doctors". Or you might also remember the character of The Sphinx in Mystery Men with his own pithy pseudo aphorisms:

"He who questions training only trains himself at asking questions."