Or at least, the language of ‘coddling’ is gendered: ‘coddling’ codes as female or feminine. This is not complicated; synonyms offered up when you Google the word ‘coddle’ include ‘mother’ (but not ‘father’ or ‘parent’). An alternate form of ‘coddle’ is ‘mollycoddle’, with the prefix ‘molly’ said to be derived from the feminine name ‘Mary’ or (relatedly) from ‘molly’, meaning ‘girl or prostitute’ [yes, really]. I also just learned that ‘mollycoddle’ can be used as a noun, meaning ‘an effeminate or ineffectual’ [yes, really] man or boy. So there’s that.
In more ways than one, the application of ‘coddling’ language to student activism echoes right-wing ‘nanny state’ rhetoric, used to criticize left-wing policies perceived to interfere with personal freedoms. In both cases, we are invited to overlay a negative, feminized, childcare-related stereotype on to something in order to condemn it.
It’s a small point, but one I’m not seeing foregrounded in current discussions about ‘coddled’ students. Once I noticed this, it helped me make better sense of (some of) what’s going on in those discussions.
Feminist Philosophers 
Perhaps “Overparenting” is the best gender neutral term which keeps the negative imagery.
I think this is an excellent point. It has historical precedent. The term “Mollycoddle” was a favorite of Theodore Roosevelt’s, used constantly in his speeches defending American imperialism, especially its genocidal policies in the Philippines. He constantly characterized pro-peace figures as “Mollycoddles”, i.e. “girly-men”, just wanting to be pampered. The term was also a favorite of Oliver Wendell Holmes–he especially used it in his speeches defending forced sterilization and euthanasia, as a means of weeding out the ‘Mollycoddle’ element of the ‘race’.