Like if I'm tryna pick a fight or start an argument. I feel like you could distract somebody like this in case someone wants to pocket something useful.
Intimidate could work. People usually focus their attention an the guy threatening them. And "Hey stupid, I'm gonna kick your ass" is generally a good way to start a fight.
Diplomacy should also work. It is the go to skill for influencing people, and an engaging speaker does attract attention. Also, if you know what not to say to avoid straining tempers you know what to say when you want those tempers strained.
Critically fail an insulting bluff check.
You want to focus their attention elsewhere, without them realising there are second motives? I'd call that a bluff.
Trolling: bluff
All of the social skills could be applicable; it depends on how you are trying to piss them off. Obviously intimidate is your most likely candidate; but diplomacy and bluff can also work depending on what you're saying and how truthful of the statement.
This. Let the player decide how they're going to do it.
Taunting is Bluff.
So you want to distract someone so someone else can use sleight of hand on them to pickpocket something?
Sounds like using aid another.
I would make it a DC 10 bluff/diplomacy/intimidate that gives the person performing the pickpocket attempt a +2 to their sleight of hand check, which would effectively increase the DC required for the creature to notice that something was taken.
The DC to notice is the sleight of hand check, opposed by their perception check.