There's no rule against it and people are more comfortable if they recline (and the chairs barely even recline nowadays). The dude is just trying to bully this woman - impose his will on her. He doesn't want her to recline her chair even though there's nothing wrong with it so he's trying to force her to do what he wants.
The dude is a tool.
She should hit the button to call the flight attendants. Plus if there's space somewhere else they might just have her move there so everyone is happy.