The electron distribution falls with an exponential function on large distances, what is much cleaner than a tree surface anyway.
Because the outer shell of electrons is fuzzy, there are multiple ways to define radius: covalent radius, Van der Waals radius and ionic radius. In molecules atoms overlap in different ways because they share electrons and electrons interact.
There still exists fundamental uncertainty about the location of atoms and molecules. Electrons, atoms and molecules have de Broglie wavelength. For molecules with tens of atoms the wavelength is in the order of picometers.
This is a bit of a long winded list of discoveries. There is no simple sophism you can utilize and say "atoms are this or that" unless you actually understand something of the background.
This Khan academy lecture is as good resource as any:
https://www.khanacademy.org/science/chemistry/electronic-str...
If I'm wrong, it would be great if someone could ELI5.
But, well, I'm having one of those days. :(
"Everything is everything."
There are naturally a lot of views about this topic, but one that resonated with me (perhaps recently discussed in HN) is that science can't necessarily make things intuitive, because it has this nasty habit of telling us when our intuition is wrong.