How can it be that private property - my own body - occupies the public space?
Which it is fine.
But unless you are totally naked, your body (not your private property) is covered by your private property and/or carries it.
It is clear that a car occupies a lot more space than your clothes and carry-on belongings, but as said earlier that is only quantitative and not qualitative.
And cars don't kill people (yet), their drivers may.