Avery wasn't the only person at risk here. Angelo and Jorge were pretty obvious accomplices if you put a little thought into it.
She didn't think Christian would expose her and risk exposing himself at the same time now that he knew Nox was aware of his identity but she didn't want to blackmail him as herself. Doing it last night as someone else had been hard enough.
She needed to come up with an excuse that seemed plausible without making it seem like she didn't want to get serious with him (even though she didn't). It took her a minute but she found a straw to grasp at.
"I can't sell my apartment. It's where I grew up and I have so many memories with my dad there," Avery protested.