I am constantly amazed by the shrieking fragility and cowardice of men who purport to be defending the strength and superiority of the masculine sex. Genuinely strong people aren't terrified by the existence of other strong people.
I'd request, though, that you don't use the word "triggered" to characterize their behavior. People like them have co-opted that word to mean "offended," but that's a profound corruption of its meaning. The term refers to a post-traumatic stress trigger, a stimulus that can trigger a genuine panic attack or flashback in a PTSD sufferer. It's a serious and deeply distressing psychological and medical symptom, and using it as a derogatory label for someone who's merely had their sensibilities offended is highly inconsiderate and inappropriate. It should be reserved for use by people who actually have PTSD, and to caution them about discussions of subject matter that could be traumatic for them.