Or to visualise how it actually happens:
Before the blade flaps up or down let's imagine that the air is flowing horizontally towards it. This will give a certain angle of attack.
Now if the blade flaps, it is moving upwards relative to the air. So the air is moving downwards relative to the blade. This downward motion of the air reduces the angle of attack.
If the blade flaps down, the opposite happens. The blade moves down relative to the air. So the air is moving up relative to the blade. This increases the angle of attack.
The key to it all is that whatever the blade does relative to the air, the air will do the opposite relative to the blade.