I have 4 kids and I hear that kind of bickering often. Usually it's common for the youngest to repeat what they hear elders or parents saying to try and put themselves in an even footing.
I know my youngest sometimes feels talked over or his suggestions passed over because, well he is 10 and they don't always make sense.

I often hear him repeating my instructions to his older brother, just because he wants to be listened to. Even if it's just about putting the computer games away.
I have no doubt it can be irritating, But I don't believe he is purposefully trying to tick you off.
Evidence being he walked away, and wasn't interested in having a fight about it.

Hope your able to feel better about yourself VO, I am certain you have any qualities you can look to and draw on.
All the best,