What is your favorite paradox mine is the Schrödinger’s cat
I don’t think most of the paradoxes out there are actually paradoxes; I think they’re illustrative of the difficulties have of conceiving of truths that run counter to their experiences. The paradox you cite is one such example; Zeno’s paradox is another; the grandfather paradox is another.
In reality, these teach us truths about quantum reality; about the nature of mathematical limits between interrelated quantities; about constraints on time travel.
Other awful (non-)paradoxes include Fermi’s paradox (intelligent life ain’t easy), Olbers’ paradox (the observable Universe isn’t infinite), or the Mpemba effect (molecules follow a heat distribution law that determines the rate of their cooling).
Philosophical paradoxes, on the other hand, can teach you something about logic, reasoning, and decision-making, and for that, the exercise is useful. If I had to pick one, I’d choose the Catch-22 paradox, where contradictory rules prevent you from obtaining a favorable outcome. But don’t confuse “unsolved problems” or “I have difficulty understanding this thing” with a paradox.