A motorcycle can only turn while leaning into the turn. If you try turning in a vertical position, the bike will simply topple away from the turn.
If you want to turn right, you have to momentarily push the handlebars to the left, inducing a righthand lean, before the handlebars go back to neutral.
Neutral, while in a turn, only means that the front wheel is following a natural curve suitable to the required arc to be followed through a specific corner.
In a vertical, straight-line situation, neutral steering will mean dead ahead.