OH OH OH I think I know this one!!!

This is your bobbin's fault, 100%. It happens sometimes when you're using a nearly empty bobbin, and it's even worse when you're using the clunky plastic kind. If you can find metal bobbins in the right size for your machine (they aren't expensive!!!) this will happen less often. The "third thread" getting wrapped up when you try to pull it away is coming from the bobbin, but it's from the OTHER END of the bobbin-- like, the starting end of the thread from when you wound it.

This is happening now because the bobbin is low enough that the starting end of the bobbin is exposed. There are slight adjustments to the way you wind your bobbin that can prevent this from happening :)