We don't want happiness for the sake of something else. We want it for its own sake. You might reply, Because I want to stay healthy. You could say, That being healthy is necessary for happiness. There is no further reason for wanting to be happy.
Happiness is just one of the intrinsically desirable things.
Moreover, Diotima and Socrates agree, the desire for happiness is universal. So really love is nothing more than the desire for happiness. I guess that Plato means to suggest two things by doing this. And second, that even the desire for happiness has, or should have, something of the same giddy, passionate character as sexual love. That's the first part of Diotima's speech, which in a way is just a restatement and elaboration of some of the ideas about happiness which are found in earlier works by Plato.