To pull birds does not mean 'to look at the ladies'. Obviously MoonKnight has never been with a girl if that is his definition. Pull birds means more than check them out it means cop off with them.
"I've not had a bit of action for a while."
"Don't worry, mate I'll wing man for you."
"Great, let's get out and pull some birds."
To check out the ladies.
Oi! Let's go pull some birds!