Am I wrong for telling my girlfriend to start taking no for an answer?

I've noticed my girlfriend has a habit of asking questions but getting annoyed when she doesn't get the answer she wants. An example of this is that on an evening she'll ask if we can play a particular video game or watch a particular show and if I say on she'll reply "Really? " then when I say yes she won't stop going on about it until she gets what she wants.

Another example is when it's her turn to wash the dishes sometimes she'll ask if I can do it. When I say no she'll keep going on about how she's tired and has other things to do to get sorted for bed and won't stop going on until she gets what she wants.

I've tried approaching it with her but she brushes it off. Last night I ended up snapping. I was sat watching tv and she asked to if I wanted to play a vdie game with her.

I said no not that night but maybe tomorrow. She responded "Really?" I said yeah I'm not really feeling it tonight and she started going on about it.

I asked her why she bothered asking when it's clear it's not actually a question. I told her she needs to stop asking questions when she can't handle hearing the word no.

I told her I'm not just here to do what she wants and that I don't have to agree to do everything she says. She said I was being too harsh but I pointed out I wasn't as she repeatedly dismisses what I actually want whenever she doesn't get her own way.

She just said i was being unfair and cruel towards her but I just told her she needs to start taking no for an answer.

AIW for telling my girlfriend to start taking no for an answer?