but we need to move it from 3° to 5° with a movement of 1° for each press
Then look at the freaking state change detection example. It does NOT use while anywhere.
You are moving the servo when the switch IS pressed, not when it BECOMES pressed.
How ARE the switches wired? You are not using internal pullup resistors (clueless, probably), so you MUST have external resistors. How are THEY wired?