What makes it so difficult to prove P =/≠ NP? — The subset sum issue
Many simple-seeming problems turn out to have solutions that are extremely complicated and deep. That's not a bad thing, in fact it's what keeps mathematics interesting. One of the best known examples is Fermat's Last Theorem, which states that the equation $x^n+y^n=z^n$ has no solution in positive integers $x, y, z$ whenever $n\ge 3$. One could hardly ask for a simpler problem, but despite the efforts of some of the brightest mathematicians it remained unsolved for 358 years! On the plus side, three centuries of trying (and failing) to prove Fermat's Last Theorem led to the development of a lot of what's known as algebraic number theory.

Indeed, the subset sum problem is easy to state. Finding a poly-time solution, though, has turned out to be really hard, to the extent that no one has yet been able to demonstrate one. One could say, "Okay, I'll turn the problem around and show that there is no poly-time algorithm possible." Ugh! That sounds even worse: how could one establish that among the infinitely many algorithms to solve subset sum, there are none that run in time polynomial in the length of the instance to be solved?

I don't necessarily recommend this, but you could just try inventing an algorithm of your own that always finds the correct answer to subset sum. You'll almost certainly find, as others have, that no matter how much cleverness you throw at the problem, you'll fail to come up with a "fast enough" algorithm. That, at least, should disabuse you of the notion that simple questions should have simple solutions.