Hey there spicy meatball,
Thanks for reaching out to the Apple Support Communities. For help with steps on how to sign out of your Twitter account on your Mac, check out the steps listed in the following resource under the "How to sign out" section that can help: How to use Twitter for Mac
If you continue to run into issues with signing out of your account after going through the steps above, we'd recommend reaching out to Twitter's support directly from this link here: Contact Us - Twitter
We hope that's able to help.
Have a great day!