Why would a man want to borrow a women’s stuff?

Was he cold?

Maybe he likes her smell and he wants the breathe it in.

Or as @janbb said, he might have been cold.

Why did he ask to borrow it? If the girl wants it back, she should ask for it back. Since they hang out a lot, it shouldn’t be too hard to get it back.

She told him, as long as she gets it back.

Hoodie is not a specific women stuff. The girl he asked from could’ve asked why he wanted to borrow the hoodie so she’s the one that get the real answer. I’ll be more puzzled if he asked to borrow a lipstick, for instance.