Servos pull a lot of current - more than the Arduino can provide.
Breadboards have tiny traces and can't withstand high currents.
So you have a double whammy: a device trying to pull too much power from a source that can't provide it, through a connection that can't handle it.
That twitching you see is another clue that the servo is underpowered.
It is true that you will see tutorials that suggest that you can run a servo connected to an Arduino, and you can, maybe, if the servo has no load. For best results though, the servo needs its own power, the Arduino just controls it.