Primarily I think Musk wants to own Twitter is because he does all of Tesla's marketing through Twitter for free, and the value of that is in the billions by it

Primarily I think Musk wants to own Twitter is because he does all of Tesla's marketing through Twitter for free, and the value of that is in the billions by itself. If he were to be banned from Twitter, as Trump has been, that would be very expensive and a risk he would prefer to avoid. Secondary reasons might include, Twitter's stock price has been in decline and it might be a good buy at this price. Musk wants to tweak the rules of the twitterverse. Finally, when it's working to his satisfaction he'll float the company again on the public markets but he'll own the voting shares so he can't be banned. He might even make a profit in the process.