What does that part about "anata" mean?

Before Doumeki used to say "kashira" (boss), using "anata" (you) is a much more colloquial way to speak, the feeling I get is that by doing that he wishes to eradicate the boss/subordinate relationship and to be seen as a worthy equal

Ahuh! I see. Thank you for explaining!

Could it be considered rude (like not using honorifics) or not really? I'm thinking about the fact that he grabbed his head before saying that so I was wondering if he was maybe being rude on purpose

Anata by itself is already a bit rude. In fact people don’t use it that much anymore if they know each other.

It’s like replacing someone’s name by you, so instead of saying
“Doumeki san, you’ve changed” which is polite, since you’re using their name he says like
“You, you have changed” which is a bit aggressive and un respect since you’re basically ignoring his name

Yeah it makes perfect sense when you explain that way! I had a feeling he was being rude even without speaking the language xD

I didn't get the chance to read the raws but I'm pretty sure he's using formal register anyways, he only deliberately chose to use the pronoun "anata" in that sentence (while I guess he's now referring to him as "yashiro san" in other parts) which is of course more intimate and significant.

The hole idea of this arc and this point in the history, is to erased the line between boss and subordinate. They aren't that anymore, they're equals, so, for the moment, the mangaka is slowly developmenting that. That's why "anata" is so important hahaha I'm expectation! I need the next episode now!

i think the translator mentions that anata is typically used by wives addressing their husbands so i assume its a much more informal/intimate way of addressing someone

I’m copy pasting a comment which idk if you read it or not so here you are:
Anata by itself is already a bit rude. In fact people don’t use it that much anymore if they know each other.

It’s like replacing someone’s name by you, so instead of saying
“Doumeki san, you’ve changed” which is polite, since you’re using their name he says like
“You, you have changed” which is a bit aggressive and un respect since you’re basically ignoring his name

Very interesting feedback! Thank you everyone
I'm still a bit unsure whether it's more intimate -a good thing- or rude -a bad thing- (haha I wish I learnt Japanese but I've already exhausted my brain cells in learning 3 other languages xD)

I learnt it from a Japanese friend, but you can google it if you want :))

It can be both, depends of the context.