I think that safe spaces / micro-aggressions may come from the perfect storm of a) a generation that was conceived after a period of widespread crime and social uncertainty, leading parents to coddle them and try to protect them from the world [see 'helicopter' parenting'], b) the self-esteem movement [everyone wins prize], and c) increasingly feminized primary and secondary education. The number of male teachers has dwindled rapidly over the decades.
I don't want to appeal to gender stereotypes but I remember seeing some research that indicated that while boys in a playground situation were more physically aggressive and directly confrontational during disagreements with each other, girls tended to have higher incidence of shunning and social exclusion - emotional/relational aggression.
Maybe we shouldn't be surprised to see safe spaces / micro-aggressions as a strategy to shut down unpleasant situations (ideas) rather than confronting them as ideas. These strategies are essentially forms of shunning and avoidance.
Regardless of how one feels about the veracity of these gender stereotypes and how they apply to the sexes, the strategies are real and they are a significant difference from what we've historically had as cultural values in the US and UK: "we're all strong enough for dissent, it's about more than our feelings."