I am kind of mystified by why this happens.
If I was asked what language the French spoke, I would say French. I would then not expect to be leapt upon by people saying a. but why are you associating French with French people, lots of Canadians speak French too, b. Not all French people speak French, some of them speak Polish/German/Chinese, stop generalising or C. why are you assuming everyone in France can speak? I would expect people to accept my generalisation. So why people leap in with the 'not all men' argument so quickly I don't know.
On the other hand, in the rise of intersectionality, we have reduced the extent to which all people in a particular disadvantaged class (i.e women, the reproductive class) can be said to have a collective experience or solidarity, so it makes sense that if there is no real sense of collective disadvantage, then how can there be a collectively advantaged group? It is all just atomised individuals and somebody saying, 'not all men...' is right.
Also, if the judgements we make about somebody and their authority to speak (i.e female, disabled) for social issues are based on individual identity rather than actual words or behaviour of the indivual to end collective disadvantage, everyone is then under pressure not to demonstrate their activism but their suffering, hence the rise of, 'Not all men... I'm a man but also grew up in a shoe box in the middle of the road,' 'not all white people... I'm white but I work in a matchstick factory next to a toxic waste dump,' etc, etc.