I suspect Quirrell's closing statements to McGonagall at the end of this chapter are not quite what they seem. I'm thinking of two in particular: the first, that he wants Harry kept away from the Restricted Section, and the second,

He set up a situation where Harry wants in the restricted section but McGonagall is trying to stop Harry. The result will be that Harry will get annoyed at McGonagall and Dumbledore for forbidden him access to the restricted section.

that he wants McGonagall and Dumbledore to try to restore Harry's mood by any means necessary.

Harry asked Quirrell to tell McGonagall that he shouldn't be disturbt. From Quirrell's perspective McGonagall is likely to do something that annoys Harry when she tries to restore his mood.