When determining whether something is wrong, I find the best thing to do is to substitute a different group of people. If it takes your breath away or you think hang on, that's quite an unpleasant and negative stereotype there - then it's wrong!
So - I won't be a wimp is what is being said. It is being said by the use of the following sentence.
"I promise not to scream like a girl"
I promise not to scream like a black person"
I promise not to scream like a disabled person"
I promise not to scream like an asian person"
It's actually not on, is it?
girl = scaredy wimp = ok?
black = scaredy wimp? would you?
disabled = scaredy wimp? would you?
asian = scaredy wimp? would you?
It really doesn't matter what it is, how minor it is seen to be, it's drip drip drip negativity and putting down and using 'girl' as a negative thing.
screaming like a girl
big girl's blouse
don't be such a girl
drip drip drip girl is bad girl is silly girl is weak...
When you see the big picture, rather than focusing on what seems at a thoughtless glance to be something very minor, you see what is really going on and that it's actually a problem.