Not all mathematical objects have correspondents in the natural world.
0 it's a mathematical convention. We can't have 0 apples in a basket. We either have some apples or we don't have any.
If 0 is weird, negative numbers are also weird. Infinity is weird. Spaces with more than three dimensions are weird.
Complex numbers are weird from an algebraic perspective but not that weird from a geometric perspective.
Empty set is weird.
Everything that's abstract is weird.
For my mind abstract algebra is more weird than calculus and mathematical analysis so that's why I enjoy calculus and mathematical analysis more.
But being weird and abstract can also be useful.