Player doesn't like recaps being done by players

I just started DMing with a new table, we're two sessions in. Traditionally, I DM in online tables, this is my first time running a game IRL. For recaps, I have the players do it to earn an inspiration and to see what they remembered from their point of view. After the game, one of the players said they don't like the recap being done this way and said that I should do the recap myself. I should also mention that this same player takes detailed notes and felt the need to takeover someone else's recap of the highlights of session 1 by adding every small detail.

I'm looking for advice for how to handle this. Do I bring it up at the table and let the players choose? Do I tell this player that this is how I run my games and this might be something they'll have to get use to?