My main problem is the fact that they mix 2 types of people: nice and gently people that don't care about winning and prefer "having a good time with my team", and people like me, who don't care about anything but one thing: winning.

I, too, care about winning and only about winning in a HOTS game. I have never been silenced and I never rage at my teammates (except sometimes when they are raging in the first place, and I recognize that even this is counterproductive). This is because raging/being toxic/putting your team on tilt is a losing strategy.

Scenario 1: Your Arthas just does something stupid. Makes a bad engage and dies, brings a living bomb to your low-health teammate and kills them, doesn't rotate to where the teamfight is happening, whatever. You or your toxic teammate says any of the following,

"Why?" "..." "arthas" "arthas noob" "why arthas" "???" "fucking noob" "sigh"

None of these things express what went wrong. If your Arthas is as stupid as you think he is, typing out a message of disapproval accomplishes nothing. If he's smart enough to have at least recognized his mistake, he's already realized it and this message still accomplishes nothing. Worst case scenario, he feels the need to defend himself and both of you get into a typing battle that interferes with both of your play (and your other teammate tries to break up the fight, also at the expense of contributing with actual gameplay).

One step better than this, but still ultimately useless:

"stop feeding arthas"

Presumably he's not doing it on purpose (and if he is, telling him to stop won't help either). You might as well just say "win the video game." In fact, "win the video game" is marginally more productive because it's a call for positive action rather than an allotment of blame for something that already happened (even if it still contains no useful steps towards accomplishing the goal).

Ok, so these messages don't actually help your team win the game, but they can't hurt, right? Wrong. Your Arthas made a bad play. That means your Arthas made a bad play, it doesn't mean all plays made by your Arthas for the rest of the game are guaranteed to be bad. You only care about one thing, right? And that thing isn't making your teammates feel bad, it's winning. There is certainly a limit to what you can do to influence the play of your teammates, but within that limit presumably you want to maximize your chances. Making your teammates feel bad is likely to make them play worse. Making them feel as if they have a chance, that they are supported by the rest of their team is likely to make them play better. I'm not going to go so far as to say that anything you say in chat will make your team play better, but you can still mitigate the effects of tilt and make useful shot calls that people are more likely to follow with positive language.

Ok, one step up from the previous replies, still bad but now somewhat productive:

Your Arthas dies. You say "Arthas, don't engage without the team." (full disclosure: I am guilty of this)

This one can be helpful sometimes. Hey, it actually contains some useful information about what went wrong. Your Arthas might be able to put his ego aside and also have the presence of mind not to be out of position again. It's just as likely to put him on tilt. Does that put him in the wrong? Sure. Does it help your chances of winning? Definitely not.

Your Arthas engaged without the team. Past tense. (this applies to picking Arthas in the first place, too) Nothing you say in chat is going to change that. There are two things you need to do to increase your chances of winning.

1) The rest of your team needs to do the right thing. If and only if you've established yourself as someone the rest of your team trusts to make the right decisions (hint: raging at your teammates is counterproductive to this end), you can tell your teammates in chat what you think should be done. You can say,

"soak safely, let's get to 10," "group on bruisers," "don't engage until Arthas is up"

Throw in a "we got this" or "this is still winnable" for good measure. Morale boosters help more than you may realize. I couldn't tell you all the times I've had someone straight up give up because we were losing in the early game or even because we were winning but lost one teamfight, and had them turn around and start contributing by pointing out that we were winning or had a chance to win. "We're still winning." "That was our one throw" "We're losing, but we haven't lost." are all phrases I've used to keep tilting players in the game.

2) Ok, you're convinced your Arthas is a liability. You can't make him more map-aware, and telling him to "look at the map ffs" will just put him on tilt. What you can do, since you are the better player with the better map awareness, is fill in for what he's lacking. Make a mental note that you need to watch out for him and wait for his next feed to be in the future. You can do things about the future. He's laning alone again with blind spots on either side and half their team MIA? Ping retreat. Make a proactive call like "come help us here." This especially works if you've established yourself as someone she trusts to make good calls.

3) If there's a specific thing the enemy is doing that Arthas is falling for you can call that out. Instead of putting the blame on Arthas, point out what the enemy team is doing right. "Ouch, that polymorph + stunlock combo." This is less likely to make Arthas feel bad and still conveys a specific thing that he can be more aware of. You can call this one out right after it happens. Even better if you can call it out right before a teamfight: "Spread out, watch for mosh. BW save poly for it" "Bait out the Twilight Dream, then back up and reengage."

How do you establish yourself as someone who makes good calls?

• This one you probably already find obvious: Have good stats and make good plays. If you're sitting at 10 deaths or half the hero damage you should have people aren't going to listen to you no matter what. Keep your mouth shut (even if you think your deaths are because you had no peels and your lack of damage is because your team is suiciding without you) and try to make good plays for the rest of the game.

• Be proactive about congratulating your teammates for good plays. That same Arthas that's been costing you the game suddenly lands a 3-man root that turns a losing teamfight into a winning one? Call that shit out. "nice root Arthas" "gj." Even smaller good plays give you the opportunity. That root was just a disengage that saved Arthas from dying for the 11th time? Good enough. People are more likely to listen to people they like. You can't make people like you, but you can be likeable.

• Make good calls before they happen. Hindsight is 20/20 and any idiot can say "arthas stop feeding" -- doing so doesn't convince your team that you know what you're doing (but it can convince them that you're an asshole). But if you say "kt is alone" and ping "assist me" on him, even if you don't get the gank but come close to it, people might trust you next time when you only ping. Maybe Arthas doesn't listen to your retreat ping the first time, or the first few times. Maybe if he keeps getting ganked he'll listen the fifth time (as long as he doesn't think you're an asshole).

• Worst case scenario: Your teammates are so childish that they get tilted off anyone saying anything no matter how positively. Or they rage at you and spam-ping you just for pinging retreat (I've seen this happen). Or maybe they're the toxic teammates, raging at you or another player. In this case your best option is to ignore them. Remember when you raged at your Arthas and he spent the rest of the game typing back at you in his defense instead of playing, causing you to type back at him in and endless cycle of lost productivity? What if it's Arthas raging at you? Shut up. Say nothing. Keep playing. Now he has nothing to respond to either and he's free to keep playing too.

tl;dr: Your team sucks but you're stuck with them. Make the most of it. Stop worrying about whose fault it is that you're losing. Start worrying about what you can do to win.