I've noticed in arguments, one party will accuse the other of 'shouting' at them.
Sam said it to Laura on Friday, Ryan was always doing it even though he was usually shouting his head off at the time
Now maybe it's me but it a lot of times the person doesn't appear to be shouting at all and is just giving as good as they get. It seems to be a tactic to undermine the other person.
It's right up there with accusing the other person of being a 'game player' on a game show.

It's massively childish, and a common deflection tactic, like 'you think you're better than me'.

It functions to close down any discussion of the actual issue and position the one 'losing' as some victim.

Ryan has a lot of childish traits - this one is 'brat', and as you say, he's the one shouting and interrupting and refusing to listen.

Natalie was another who would ask someone why they're shouting at her - whilst she's bellowing at them!