Why don't Ron and Hermione make a good couple? Because there always arguing, that's all they ever seem to do. There complete opposites as well and Ron could never hope to compete with Hermione's intellect.

Why are they always arguing? In the first book, its more Ron bulling Hermione and she having a bad opinion of them, due to what they do. No true arguments, nor in the second book, now that I think about it. The third book did have a lot of arguments, but mainly about their pets and nether due to differences of opinion. I can't think of a single argument where they deliberately insult the other. Mainly they argue over studying habits, I can't think of anything else of the top of my head.

In which ways are they similar? They are both obsessed about different things. Ron is obsessed about Quiditch. Hermione is obsessed with rules and reading, actually no that's not right. Hermione is obsessed with achievement, getting the best possible grades to get the best possible job. Ron wants to be seen for his own person, he wants to be recognized as himself rather than Bill's younger brother. In a weird way their goals overlap.

Intellect? Many people myself included state that Hermione would have to explain everything to Ron, because he's so thick. But actually Hermione is weeks if not months ahead of her year group. So everyone is going to seem stupid to her. That does not mean that Ron couldn't have a conversation or even debate with her. But why would she want too? She doesn't debate topics, really anyway.

So really why shouldn't/couldn't they live together. No reason in all honesty