tldr
it's literally been years since I heard someone use 'gay' as an insult unironically. some people use 'friend' but I don't think a friend is necessarily gay. there are lots of straight cigarettes
I think the general idea is that they want to do the work at school instead of home because thats what you would be doing at your job. If your doing your work at home they could see it as a sign that you didn't work hard enough to get the job done at school/work. It's stuffty but that's one of the ways they probably view it.