Why is it that a player can be banned for petty things like arguing or expressing rage in some way or form.
Because the vast majority of players believe this has no place in League of Legends.
and if you type in anything remotely human (because that's what free speech is), you get hit with chat restrictions or bans.
No, that's not what free speech is. You have freedom of restrictions on speech from your government, not a private business or individual. Businesses and individuals can refuse service and/or kick you out for any reason they deem necessary (save for your membership in a protected class, of which asshole is not). Further, "being human" is not the same as being an asshole.
Why do I not have the right to speak my mind?
You do. Riot also has the right to kick you off of their servers.
The line truly isn't that fine that Riot has to issue the same penalties for people that do seriously harass or speak in a prejudice way as those who are arguing.
They don't. People with less severe toxicity take more games before they're finally punished. People with more severe toxicity are punished after less games.
This is a video game, not some political crossroads where we have to delegate superior moral behavior.
Riot is not "delegating" (wrong use of this word, by the way, I'm not even sure what you were trying to say) anything. Riot is simply setting very common rules - don't be a dickwad, and you won't get banned.
I have spent countless hours and real life money on this game
And this means you should have the right to ruin other customers' games? What if the person who you pissed off spent more money and/or time than you?
only for some sensitive kid behind his keyboard
You mean you? You're being sensitive here - you are getting unhappy just because people want you to not be an asshole in game. You are also behind your own keyboard.
to prevent me from playing or typing because he hits the report button in attempt at revenge.
You are not punished if you do not misbehave. You can be reported hundreds of times and if you don't misbehave you will not be punished. Simple way to not get punished - don't misbehave. Over 80% of players succeed at never getting a single punishment.
Why have the ability to chat at all, if everything is monitored and judged in a dystopian manner.
Again, over 80% of players never get a single chat restriction, much less a temporary or permanent ban. Nothing is managed or judged in a "dystopian" manner. It's judged with the eye of "don't be an asshole". It's not hard.
it feels really bad to have it taken from you because of some petty social standard decided upon by other humans.
I suggest you follow the rules of a community you decide to be a part of then.
but in all honesty if someone can't handle what is literally not only normal on the internet but in real life why are they playing a game where socializing is one of its greatest merits
Being an asshole in real life is not "normal". You are free to socialize in League. I suspect highly that your form of "socializing" is something you consider normal but the rest of society in real life would consider vile, disturbing, and/or plain disruptive.
We're not all going to be these weird robots only promoting positive remarks like "gg! Well played! Good job!".
Nobody expects you to. It takes a hell of a lot to get punished. I've had my moments in games where I say something that isn't really very nice. I have not gotten a single chat restriction ever across multiple accounts. You're allowed to screw up. But when your screw ups are either severe, consistent, or persistent, it becomes a problem.
There has to be some level of criticism allowed
There is. In fact, you will never be punished for constructively criticizing others in moderation and when it is merited.
and if argument will always result in penalty the initiator should be the one punished.
Both players are participating in toxic behavior. Both players are at fault. Your lack of self control and your retaliatory nature are not other players' problems and other players should not have to suffer because of it.
With that being said, I'm considering quitting this game due to these foolish standards
You are free to do so. I encourage you to reflect on this because society's standards are no different. In other words, you'll have a hard time in the real world if you think Riot's standards are "foolish".
and will explain why to the literal 100s of friends I have that play this game
If your friends are normal, they may agree with you to your face, but in private they'll think you're an idiot and a jerk because you got punished and instead of accepting it and becoming a better person you decided to whine and moan about it. If they're toxic like you are, then Riot would rather them leave the game anyway, so you're doing them a favor.
Many of which will surely do the same because they play to spend time with me in a fun way.
Why is your fun so much more important than that of the other 4 players on your team?