I wonder why Stack Overflow doesn't allow a user to sign in with Twitter. Could there be any technical reason or is social login with Twitter not so popular/useful?
The short version is "Every provider we support adds a ton of overhead in both implementation and support."
There are a couple other considerations (we don't require an email, but it's a nice to have - especially for account recovery, for example), but having said that, the last time we looked at what it'd take to support Twitter-based authentication was a couple years back. Things have probably changed some since then, so it might be worth revisiting, but if I'm honest, it'd take a very popular request at this point.
FWIW, my personal preference, as someone who has done extensive work on our auth and recovery code, would be to reduce the number of credential providers we support rather than add another one at this point.