I wouldn't claim Twitter will shut down soon, but one could argue that mastodon is more robust because it's divirsified.

There's no single person on earth who can shut down Mastodon, so Mastodon dies only if this decision is made massively by many people (or if development stops, but then still nothing will stop the server I run on raspberry pi in my bedroom). Twitter otoh can be shut down by one person for a whole multitude of reasons without any concern for the opinion of users.