Given the discussion above about pushing and pulling on the stick, I'm minded to point out that the stick is connected to the less (perhaps, least) powerful pitch control on the airplane.
An awareness of the stab position and movement and, for aircraft with a pitch/power couple, the thrust, is essential. Either or both of these may have played a role, or be playing a role, in creating the situation you're in.
Stick-neutral is stick-neutral, not pitch-input-neutral.
Stab position and/or thrust may very easily overwhelm the stick input.
You may need not only to move the stick, but make aggressive changes to trim and/or thrust too.