I think you're missing the mundane explanation. Harry really likes Quirrell. He's the person he most relates with in the world; he's the person he looks up to; he's the smart/strong/cool teacher Harry wants to be when he grows up.

Surely there were other people, maybe better people, to trust and befriend? Professor McGonagall, Professor Flitwick, Hermione, Draco, not to mention Mum and Dad, it wasn't like Harry was alone...

Only...

A choking sensation grew in Harry's throat as he understood.

Only Professor McGonagall, Professor Flitwick, Hermione, Draco, they all of them sometimes knew things that Harry didn't, but...

They did not excel above Harry within his own sphere of power; such genius as they possessed was not like his genius, and his genius was not like theirs; he might look upon them as peers, but not look up to them as his superiors.

None of them had been, none of them could ever be...

Harry's mentor...

That was who Professor Quirrell had been.

Any person, especially a child, will gladly ignore and forgive a million counter-indications as long as they really like the person.