She gets on my nerves!!

This situation is more complicated than him just trying to help her out while her father is physically assaulting her. He did not have to go straight to bashing his head against a wall. I don't want to say, her father was 'just' holding her by her hair because that's already more than enough to call for intervention, but he could have easily restrained him without jumping straight to attempted murder.
Siyun is way too comfortable with inflicting serious bodily harm on those, he thinks, have wronged him or Jeongmin in any way, up to the point that he'd be comfortable with murder if that is what it takes.
She a) doesn't want him to potentially go to prison, b) have him hurting people she cares about (her father might not fall into that category but others Siyun hurt before do) and c) she doesn't feel comfortable being with someone whose first solution to every problem is violence. Most normal people wouldn't and shouldn't be comfortable with a person who is that quick to hurt others.
She isn't a therapist or phsychiatrist so she does not have the means to handle him appropiately, although I am giving her credit for trying her best regardless. Helping Siyun deal with all of his issues is still way above her paygrade and is gonna blow up in both their faces sooner rather than later.
They both need therapy and lots of it, too.

When siyun was hurting innocent people he was definitely wrong. But I'm thinking jeongmin is getting a little too comfortable with telling him he is wrong all the time especially when we see how much he has changed it's a huge leap

If we are being realistic here and we are looking at the characters in a realistic way.
No one would just let there love one get dragged by their hair in front of them , you would instantly get physical what was he supposed to do/say? "Stop let her go please your hurting her!" And that wouldn't have worked

Was it the best response in the moment? Probably not
Most people don't act all that rational in a situation like this. And again, it's way above her paygrade. You can not expect her to always say the right thing in the heat of the moment. I actually think, he needed the wake up call that she is serious, and either he gets his shit together when it comes to reacting to everything with violence or she's out of there. But that's just my two cents.

Siyun is physically fit and had the moment of surprise against a drunk old guy. Take him into a chokehold or something, anything but straight up bashing his head against the nearest wall. That would have definitely worked given the circumstances of the situation.

I definitely understand where you are coming from
To me it was better he did action instead of no action at all and true a chokehold would be better

She has been overlooking and dismissing a lot of stuff which mostly lead to him making drastic choices/not knowing better (still doesn't make it right)

But at the same time they were both wrong at some point
I just hope her character development gets better because at least he is trying for her
Trying to reconnect with his family
Trying not to be obsessive and respect her boundaries
Even apologizing to people

Girl didn't even notice the change she thinks he's the same because he decided to protect her
It's just the vibes she gives off throughout the story and the things she says.

However I do hope she at least sees he is trying to make a effort for her in the story she just
Seems very nonchalant

At first I loved her character but as the story progressed ehh
Not once did she get pointed out for her wrong against him by him

But if that boy even look at someone wrong she down his neck

This is the only reason I'm dropping this manga because it's the same cycle of her basically saying "bad dog"
I love his character development but her development is barely there
I'm not saying she hasn't changed because she has!
But at this point the girl is ok with bad happening to her and he bet not dare act when bad happens to her or it's "bad dog " cycle again

If she at least see his efforts I would willingly keep reading