We don't say that one person is falling out. Two people fall out.
Most often, it's a noun phrase: Lucy and Paco are having a falling out.
As a verb phrase, we might say: Why did Lucy and Paco fall out?
So she wouldn't say she's falling out. That wouldn't make sense. More likely:
- I'm taking a break. I'll call you when I want to talk to you again.
- I need a time-out. Don't call me for a while, okay?
- Let's take a breather. I really don't feel like dating right now.
- I need some space. I'll text you when I'm ready to get back together.

English Teacher