I think that it is just hard for a lot of men to "get it". I just watched the latest episode of The Good Doctor on Hulu and the episode was an elegant presentation of the problem with how men aren't expected to empathize (they quickly forget the emotion context for others) and women, since they are better at it, get tasked with doing the relating in a relationship.
Very well done episode and can stand alone if anyone is interested in watching. It is Season 3 EP3 "36 Hours".
The point being that men grow quickly uncomfortable with criticism in this area of empathy because, well, the masculine, separative ego mode of development is used to resolving conflict by authority and initiative and otherwise dominating. But this mode fails when it is not necessary to win in a relationship but to come to a consensus or mutual understanding and respect. Women are continually, by default, those that have to keep the peace while the "boys" fight it out. As a result women "lack initiative and aggression" but if they exhibit these qualities they very quickly are criticized for being irritable and in a mood of some sort.
This is perhaps why you think the sensitivity barometer is hypersensitive...for many women it has gone from hopeless to annoying.