This is very common and I'm sure we've all come across these analogies. For example...
If you defend the right of individuals to wear what they want, eg skirts, bikinis etc, then many Muslims will say to you... "Would you like it if your mother or sister wore these things?"
If you defend the porn industry or the right of nudists and topless models then again they will say the same thing.
There seems to be a general consensus amongst Muslims that if we wouldn't like something for our own mothers and sisters.... then it should be banned from society for EVERYONE.
This is a subtle but significant slight of hand because it presupposes that a like and dislike are equal to a prohibition. The root of this problem is the contest between individuality or atomization and communalism. Individuality states that every person has the right to do as they wish so long as it doesn't harm another person, and the response to a harm should proportional to the harm. The question the becomes does porn or not wearing the hijab harm anyone else? No of course not. So it shouldn't be even be a question of "would you care if your mom did X or Y, because her decision over her life outweighs any other superficial capricious desires of others.
People do lots of things that we personally don't like, but a person's right to live their life how they choose is more important that hurting some one else's feelings.
ALSO...
It’s well known that Muslims are supposed to love Muhammad a LOT. More than their own mothers infact.
So to prevent non-Muslims from insulting or even criticising Muhammad, many Muslims will say "How do would you like it if somebody insulted your mother?"
How would you answer that? Would you desist from criticising Muhammad because it's apparently worse then insulting someones mother?
Is that a valid reason to NOT criticise or insult Muhammad? What if somebody out there loves, say, Hitler more than his mother. Would this mean that we must all desist from criticising Hitler?
There is a difference between civil conversation and authoritarian demands to be free from criticism. In civil conversation people don't insult other people's mothers that so that a mutual exchange of conversation can happen, in other words "civil conversation". This doesn't mean that there should be any law against insulting a person's mother, nor should there be any criminal punishment. You can't constrict freedom of speech because by doing so you create the reasoning to restrict you own freedom of speech.
For instance, I love humanism and liberalism. Should I be allowed to imprison and fine those who critique it or insult it?
Topic: "Your mother" and "your sister" analogies used by Muslims