Why is P vs. NP so hard? Why is $\mathsf{P}$ vs. $\mathsf{NP}$ problem considered so important?

Is $\mathsf{P}$ vs. $\mathsf{NP}$ the hardest mathematical problem? 

Why is it so hard?

All I'm looking for is the hindrances to solving $\mathsf{P}$ vs. $\mathsf{NP}$. Are there any theorems that help explain why $\mathsf{P}$ vs. $\mathsf{NP}$ is 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.