You don't need to know why she wants a day off. She has a right to ask for days off. It is none of your business why.

Not sure why it's your concern about why she needed that particular day off and yes you could have easily sent her a text with yes or no.

maybe she wants you all to herself

Yes, you were - you promised something and didnt deliver. Letting it slide til you saw her again meant she was uncertain about it, and she probably has some sort of planning or coordination that depends on the answer - maybe she was trying to book a ticket somewhere & there was a timeline on it, forinstance?

I’m assuming if she texted you and didn’t just wait to ask you in person she needed to know asap

Is it hard to text her a yes or no? That would be considerate of you.

If you said you'd get back to her and didn't then, yeah you were in the wrong.