Self-hosting can be a good way to make sure that your privacy and security are protected.
People do this with platforms like Nextcloud, which is a platform where you can host all your files, images, calendars, and anything else that you would use a cloud suite for. This is a good reason to self-host; you are not relying on anyone else, and there is no chance for tracking.
Some people self-host things like SearXNG, which is a metasearch engine that uses Google, DuckDuckGo, Brave Search, etc. I don't recommend self-hosting something like this, as instead of just giving a fingerprint of you to, say, Google, now you are giving it to many different search engines.
The way they are supposed to be used is that many people will use the metasearch engine, and so the actual search engines can't differentiate between each specific user and can't track any of them. If it is just you using the platform, then each search engine can know every search request you make and thus make a profile of you.
This has the same effect if you use something like a frontend to a website, like Nitter, Piped, ProxiTok, etc. The only reason to self-host a frontend is if you are going to get >10 people to use it, so the platform you are using can't know who is who.