Why is P vs. NP so hard?
I guess the best answer to your question is to point out that there have been several "barriers" to proving the P vs NP problem which have been identified and which rule out a number of approaches to a proof.

The three main barriers identified are relativization, natural proofs and algebrization. All of these are described on the P vs NP Wikipedia page under the heading "Results about the difficulty of proof", here.

A more detailed explanation can be found in the papers outlining these barriers referenced on the same Wikipedia page.