Can we celebrate an anniversary without agreeing which day counts?

I put a heart beside the date of our first date in the kitchen calendar. My partner crossed it out and moved it to the day we agreed we were a couple. "That's our anniversary," she said. I hadn't known she felt strongly about the distinction.

I remember the first date because we talked until the cafe stacked the chairs. She remembers the later conversation because it was the first time she felt sure what we were choosing. Both memories mean something to me. Neither date has been an established annual celebration yet.

I suggested celebrating both. She said that sounded like a way of avoiding a decision, and that she'd rather have one day we both call ours. I don't want to fight over a calendar or make her important memory feel secondary. But crossing out mine felt strangely dismissive.

How would you choose a shared tradition when the two of you attach it to different beginnings?