There are different ways to get what you want. One of the most insidious is using emotional blackmail, and it's ilk.
At it's simplest, the tactic consists of saying: "if you don't do what I want, I will leave". This happens in marriages all the time, and it happens in online communities all the time too. Let's say, 2 (valuable) people take a dislike to one another, and they both come to the site administrator/arbitrator and lay their demands on the table: "if he/she/it stays, I go!". The arbitrator can only lose, the community loses. If a wife (traditional values alert here), says: "it's me or the nudism", what does the husband do? He can only sacrifice 1 of the 2 things he holds dear, the question becomes a measure of worth, and in either case, he loses.
The more mature approach would be to try to come to some form of compromise. To explain why you are dissatisfied/discontented and to try to get other people to see your,or another, point of view. Perhaps some options have not been discussed, or even thought of. As a moderator on several sites, and the administrator of others, I see this all the time. People come to a unique community, and then demand it changes to suit their preconceptions. Running off in a temper-tantrum if they see anything they don't like. "I'm not staying here if..." Simply running away, (turning your back on the community), or sticking your head in a hole in the ground, does nothing to change the status quo, in fact it often makes things worse.
Firstly, it plays into the hands of the very people you are disagreeing with, by permitting them to win by running away. Secondly, it provides no opportunity for discussion of the very issues which need discussion. Thirdly, and perhaps most importantly, it deprives you of the very platform which you so eagerly joined in the first place. The question quickly becomes one of: "Do you actually want to change anything, and if so, how are you going to do that by not being 'on the spot'?"
If this platform is, (let's say), an online group you joined one day and left the next, perhaps it's no big deal. Easy come and easy go. If, however, the platform is one in which you feel great personal connectivity, many ideas are expressed there with which you feel close affinity, then the commitment is all the greater. One might liken it to a marriage of a decade or more. Now, are you going to leave because someone said some one thing with which you disagree, or are you going to stay and try to modify the (in your view) errant opinion? Perhaps it could be pointed out that the phraseology was judgemental (for instance), even if the issue was clearly valid. This is not always an easy call, as some issues are clearly deal-breakers, and it's better to find them out early rather than later, (I speak from bitter personal experience). Nevertheless the decision might need to be considered rather more than in huff-mode.
All in all, threatening to walk away is usually a lose-lose, scenario, for everybody.