"Not my Nigel" is a shorthand description for a common defensive reaction of many women to feminist observations and explanations of widespread sexist activity and sexist motivations, which is that while certainly some other men are oppressively sexist, their particular partners/sons/fathers/brothers couldn’t possibly be part of the problem.
- i.e. “Not my Nigel! He’d never do anything like that”
or more invidiously
- “well sure, my Nigel says/does that but he doesn’t mean any harm by it”.