If everyone believes P ≠ NP, why is everyone sceptical of proof attempts for P ≠ NP?
People are skeptical because:


No proof has come from an expert without having been rescinded shortly thereafter
So much effort has been put into finding a proof, with no success, that it's assumed one will be either substantially complicated, or invent new mathematics for the proof
The "proofs" that arise frequently fail to address hurdles which are known to exist. For example, many claim that 3SAT is not in P, while providing an argument that also applies to 2SAT.


To be clear, the skepticism is of the proofs, not of the result itself.