"Why is it okay for a player to start 0/6 in 10 minutes, but not okay for other players to address the player about the behavior?"
Feeding is definitely not okay, but if it's feeding because of poor play rather than a more intentional variety then there's really no reason to go so far as you do later and call it "toxic". Addressing the behavior is okay depending on when and how it is done. Specifically, I consider it feeding after about the 2nd or 3rd death without picking up a kill or assist in the process, dependent mostly on the timing of things. As an example, 2 kills can be feeding if you die to a level 2 or 3 all in, return to lane, make a stupid trade due to tilt and die a second time right away. At this point you have fed your enemy laner and need to change your play immediately to avoid continuing to feed. This is when you need to be talking to this person (calmly) and strategizing with them to prevent further feeding and possibly even bring them back into the game with good ganking. If you just say something basic and unhelpful like "stop feeding and farm under tower" you will do nothing but tilt them.
"Why is asking them to stop playing in a way that got them to 0/6 in the place, or suggesting they stop playing ranked considered toxic behavior, rather than the player that generated the frustrating situation?"
Asking them to stop without providing reasonable and effective solutions to the problem in the process is completely meaningless, and typically comes across as douchey, thus why it is considered toxic.
Based on your clarifications of what "stop playing ranked means": First, telling someone to "stop playing ranked" or just "stop playing" does nothing for the current game, other than probably tilt them even more because now you're telling them they're tilted and it just becomes this vicious downward spiral of tilt. Second, hoooooooly crap that phrase is super easy to misinterpret. If you only say "you're tilted, stop playing ranked" it definitely sounds like you're effectively using the old "you suck, uninstall noob" line. Definitely work on your phrasing with that, and definitely save it for when the game is over.
"Why is a player allowed to start 0/6, sink the game in laning phase and then hold their team hostage in the ff vote until 20 minutes?"
Normally I'd talk about how throws can happen so it's not good to throw in the towel too early and blah blah blah, but given the specific example and the "holding their team hostage" bit I think you may actually have a bit of a point here. There's literally no good reason to refuse to surrender if your team is getting hardstomped, or even if the entire team has given up and you are not the person with the best ability to carry the game back from the brink.
"Lastly, why are these two activities defined the way they are under the current behavior moderation system. It seems like a poor way to address toxic behavior IMO. Thoughts?"
Actually holding people in a game far beyond when it should end should definitely be considered griefing and be met with harsh punishments. I don't quite think the 5 minutes between unanimous and majority surrender count as that though, even if they are painful and unreasonable.
As for feeding from poor play, well, if you consider that behavior toxic then you really need to reevaluate your definition of the word, and also your mentality when playing ranked. Poor play is not toxic, you tilting because of other people's poor play and ranting that they need to be punished by riot is super toxic. Why? Because people have bad games, and it is stupidly unreasonable to expect that they always avoid their bad games whenever they're teamed with you. Sure, there's a level of skill you expect to see, but you shouldn't go tilting the earth into a new orbit just because you don't see people playing to your expectations every game. If other people's poor play is actually tilting you and ruining your enjoyment of the game, I highly recommend stepping back for a bit and looking up some guides on managing tilt and dealing with bad teammates so that you can start enjoying ranked again, because the bad players aren't going away anytime soon.
Edit: I removed a bit about telling people not to play ranked and have replaced it with a better response to the situation based on the comments in the thread. Also re-added some parts.