I'm going to go out on what might be something of a limb and suggest that perhaps Twitter is not the place for meaningful discussions, or even, discussion in general.

Obviously there's no right or wrong way to use Twitter, but I generally don't follow people who do more than post inane status updates like "i love tacos lol" or links to mildly interesting news articles. For me at least, that's all I want Twitter to be, and it does that admirably. If I want discourse theres room for that pretty much anywhere else on the Internet.

I suspect the majority of the problems people have with Twitter stem from expecting it to be something that it just fundamentally isn't and can't be. If you use Twitter with a desire for serious engagement with others you're almost always going to be disappointed. If you treat it as a place to put silly 140 character messages out into the world whenever you feel like it then it's much more fun. And weirdly, much more useful.