Can we get a laymans explanation of what this is about? I understand what p np is, but don't really understand what this person is claiming. Is this some kind of claim about the overall concept of p np? Or proving a specific case?
Proving an inequality is "easy", because only requires a single counterexample: if there is one problem in NP that is not in P (I.e. an NP problem not solvable in polynomial time), then NP can't possible equal P.
Fukuyama is proposing that CLIQUE is such a counter-example.
(Proving the inequality doesn't actually require the special property of NP-completeness which others are talking about; that is only useable in a proof P = NP.)
Proving an equality isn't exactly "harder" (no NP-hard pun intended) - all you have to do is show that a single NP-complete problem can be reduced to a problem within P in polynomial time.