Is it impolite to refuse to share your umbrella with a stranger when it's raining?

I know! You get the strangest reactions! It’s only an umbrella, right? The last time I asked someone, she screamed and ran away. You’d think she’d never seen someone wearing a hoodie before. I even spoke in a whisper to not seem threatening. And it wasn’t even raining! It’s not like she would have gotten wet.

“Is that your shiv or are you happy to be dry?”