There are two main things that put me off trying to use Twitter: the character limit, and the closed nature of the platform.
The character limit is a completely backwards concept to me. Yes, it encourages people to be succinct, and yes, it creates a space where short-form content feels like a valid contribution. But almost every tweet I get linked (through friends or other websites) that's interesting is either a pointer to another website, or a thread. In order to say anything useful on Twitter and actually have a conversation there, people have to butcher their prose into a thread of sometimes garbled sentences. For me, it's not pleasant to read and it's even less pleasant to write. People work around the limitation by creating images of long-form text (great for accessibility /s) or, like this piece, writing their contribution somewhere else and then just linking it on Twitter.
Being a closed platform isn't just a philosophical issue. It means I don't feel like I own my content. It means I am at the whim of the company's dark UX patterns aimed at driving 'engagement', like forcing visitors to log in to view a thread.
Why would I want to participate in a platform that is so hostile to allowing me to have meaningful conversations?
I have my own website/blog where I have complete control and ownership of what I write. My website is open, mobile friendly, and lightweight, so anyone can go and read it without waiting for a spinner or with a modal getting in the way. I have an email address on there so any visitor can contact me. Occasionally people email me and we have a chat.
I network through email. If I discover someone's work and it's interesting, I send them and email with more than 280 characters explaining what I got out of it, sharing my own thoughts, and pointing them at other resources and people they may find valuable. Friends and colleagues reciprocate and send me interesting stuff. Sometimes we have a video call and catch up and discuss opportunities to collaborate.
I sign up to people's newsletters, and subscribe to journal alerts and mailing lists. My inbox is a steady stream of interesting conversations and announcements.
I skim Hacker News, Tildes, and MetaFilter for new links. I read the comments because usually people are insightful and the interface is clean and lets me focus on the content.
I could probably get some use out of Twitter as a way to stay up to date with specific people, if I wasn't so turned off by the UX. A service that allowed me to follow people and then just emailed me a daily or weekly digest of tweets from people I follow (maybe ordered by some metric like retweet, which I also don't grok) could be cool.