Your comment and the OP act like the Tellarites don’t like anyone, but that’s not really true. The Tellarites and Vulcans got along just fine before Humanity showed up. The Vulcans probably figured out the Tellarites’ gimmick and decided that challenging each other’s ideas was how they arrived at a logical conclusion. The Andorians were probably too hot headed to get along with people who challenged them on everything, leading to them being in conflict during ENT.
As for how humans fit in, humans may be crazy bastards, but they also occupy a nice middle ground between the others. We can be as emotional as Andorians one day, as logical as Vulcans the next, and a number of our political systems were built on Tellarite-style arguing. Humans can hear out one ally, then explain their position to another in terms they’ll understand. We can also tell when Vulcans are secretly being driven by emotion, can leverage Andorian emotions to bring them to a more rational perspective, and debate Tellarites on even ground. Humans are the interpreters and negotiators that got these people to actually talk about their problems with each other and come to a reasonable compromise.