Yet every left person I heard with an opinion on the matter has said something along those exact same lines.
its like saying that a robber has the right to shoot someone they are robbing just because they pulled a gun on them. what rittenhouse was doing isnt legal in the first place.
Neither of us clearly are lawyers, but it's not at all like a robber shooting you and claiming self defense. You're trying to invalidate his claim to self defense, but the specifics of the illegal act matters a ton. Jaywaking, performing tax fraud, smoking pot, or speeding wouldn't invalidate your right to self defense but breaking into a house would. Raping somebody would remove your claim of self defense. Context matters, but the pattern generally seems to be violent crimes invalidate it.
what rittenhouse was doing isnt legal in the first place
You'll have to be more specific, but I'm guessing you're saying he shouldn't have had a gun crossing crossing state lines. That's probably true, and he'll probably be prosecuted for that. But that doesn't invalidate the right to defend yourself. My understanding is he also worked in another state, so this isn't like a case of he decided to drive to a random state specifically just to cause trouble. Honestly his "crime" is a completely victimless crime and would probably be ignored were it not that he got caught up in this riot and the nationwide case. That was indeed poor judgement on his part, but he still has a right to defend himself.
he has the right to defend himself, i dont think hes deserving of a conviction for first-degree intentional homicide but i think he is potentially deserving of a conviction for reckless homicide or manslaughter because his poor judgement led to people getting killed. he decided not to disperse from an unlawful assembly, to be a vigilante (the legality of which is questionable), open carry a weapon as a minor, and have a gun of questionable ownership and legality. if it was his property he was protecting i'd believe in castle doctrine personally but we dont have that as a law here.
theres certainly a fine line between overuse of force and underuse of authority by police. just because they werent exercising their authority to the extent kyle saw fit doesn't mean he should have taken the law in his own hands.
Rittenhouse was attacked. He shot no one before the attacks and no one after.
That is not "an eye for an eye justice". That is self defense and self preservation. Self defense is a human right.