Why is my neutral wire connected to a breaker?
That's not a neutral, and this is not a correct/compliant/safe installation.
Your well pump is 240V. Cable comes black, white, ground and when you have a 240V only load, the white wire is a second hot. In conduit, you would use a hot color (2 blacks, or black &amp; red, or one of the various other colors) but in cable, 2 conductors is black &amp; white.
It should be &quot;re-marked&quot; with black or red tape or paint or heat-shrink, but it often isn't.
It should NOT be connected to two independent breakers. It should be connected to a dual-pole breaker which will be twice as wide as the single-pole breakers you show, and clip onto TWO of the bus wings.
[want proof? turn off your shed breaker and watch your well pump not run. But you might find power in the shed, to an extent (at least enough to shock you) if the well pump is trying to run, since power will pass through the motor windings (at half-voltage) and then to your shed circuit - this Not Good.]
So, buy a dual-pole breaker of the correct size for your pump, re-mark the white wire with red or black, and connect the well black and re-marked white to the two terminals on the new dual-pole breaker, leaving your shed circuit out of the well circuit.
You'll have a 20A single pole breaker (that you will remove the black pump wire from) to use for whatever new thing you are adding...
Obligatory reminder to use a torque screwdriver or wrench for tightening the terminal screws - values are on the box label, and molded into the breakers themselves (35 in-lb for the breakers, if I recall correctly)
Further issues, responding to comments.
Yes, the neutral being double-stuffed is wrong. Every neutral gets its own hole. Grounds may be able to share, that should be detailed on the panel label that also has the torques for the ground/neutral bar screws.
The well breaker should be a double-pole, probably 15 or 20 amps, size should be specified in the pump's documentation (if you have it or know what it is.) If it's not tripping the 15A shed breaker that feeds half of it, 15A might be sufficient (if documentation is missing.) Looks like you could put that on the bottom and move the shed up - or you can wire-nut an extension onto the well white to make it reach the top position. Breaker panels ARE junction boxes, though there's a common misconception that they are not.