The fundamental geometry of a bike causes it to self correct when it’s in motion. It may not be immediately apparent but when you turn the handlebars the ground resistance against the front wheel turns it in such a way that it’s restored to upright and straight travel. This is mainly achieved through the angle of the front forks relative to a perpendicular to the ground axis.
This can be easily seen if you send a bike careening down a road at speed without a rider. It might wobble yes but it generally comes back to being upright, and you can see it happening as the bike leans and weaves but ultimately comes back to going straight.
When you’re not moving you lose this force acting on the bike so it cannot stay upright.
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