I'm probably missing something but I don't quite understand the Antagonize feat, in comparison to using intimidate to demoralize a target. For the cost of a feat that can only be taken at level 5, I can apply the off-target condition. This is in comparison in straight up using demoralize to impose the shaken condition, which has more penalties and doesn't take a feat.
Other than I can use diplomacy in place of intimidate, what am I missing here?
Antagonize is more about tanking than debuffing:
Both are debuffs that lower attack bonuses (protecting your party), but antagonize can be easier to land vs targets that have high intimidate scores themselves (often hard-hitting bruiser types), and also provides an incentive for that target to fight you specifically (ie tanking), as choosing to attack you cleanses the debuff.
Demoralize is similarly easier to land vs targets with high sense motive, has the bonus of reducing saves on top of the other penalties, is language-independent, and does not cost a feat.
Antagonize is a slightly weaker shaken with added tanking utility that is used less to debuff and more to attempt to control the opponent's actions. It trades off power for control, which might be preferable if you have high enough AC that it can be difficult to get things to target you.
If you know that the DM will ignore you anyway, shaken is the better debuff: but they actually stack, so you can hit them with both and at least they'll be attacking everyone else at -4, maybe throw in bodyguard for +2AC to anyone they attack and it starts to add up, and then in harms way if anything does get through, etc. etc.