Maybe the son is just being silly and thinks it's a funny thing to ask, like a childish prank.
The mom could be shocked at first but then gently explain to the son that it's a private and natural but not something to be begged for. For instance, she might say that farts are a normal body function but not something we should play around with in this way. She could also use this as an opportunity to teach the son about good manners.
One possible reason could be that the mom always wanted a daughter. Maybe she had dreams of doing girly things with a girl like shopping for dresses or having tea parties. Another reason might be that she has some unfulfilled desires from her own childhood related to femininity and is projecting them onto her son.
Maybe in a fashion - related story, the mom is helping her son with a school play or a costume event where stockings are part of the outfit.
One possible reason could be that the mom has some traditional gender - role ideas that are a bit twisted. Maybe she thinks that boys should be more docile and 'feminine' in behavior. Another reason might be that she is over - controlling and wants to shape her son according to her own strange vision of an 'ideal' child. It could also be that she is unconsciously projecting her own unfulfilled desires onto her son.
This is an extremely inappropriate and unethical topic. Such a situation is abnormal and goes against moral and social norms.
One reason could be financial gain. Maybe the son wants more money for luxury items or to pay off debts and he thinks blackmailing his mom is an easy way to get it. For example, if he knows she has a secret savings account she doesn't want anyone to know about.
Another reason could be related to education. In some cases, moms might check as part of teaching their sons about basic body parts and hygiene. This can be an awkward but important part of growing up for a boy to understand how to take care of himself in that area.
One possible reason could be for medical treatment, like if she had to undergo chemotherapy. Chemotherapy often causes hair loss, and some people choose to shave their heads preemptively.
Greed could be one reason. If the son is money - hungry and knows his mom has something to hide, he might blackmail her for financial gain.
Perhaps it was a cultural difference. In some cultures, young children may bathe with their parents for practical reasons like limited facilities. But this should be within an appropriate age range and still respect privacy.