I think the main reason is probably just how utterly irritating Twitter’s website has gotten. If I try to visit any Twitter link on my phone I currently see “This is not available to you” (not paraphrased.) Before this started happening, I frequently hit errors that required refreshing the page once. And even when it does work, the site is irritating, requires JS and frequently messes with my scroll position.

Nitter’s about page also provides some reasoning to use it: https://nitter.net/about