This answer confused me at first, because I initially thought you were trying to say non-fungible assets can be divided. At least in the case of non-fungible Ethereum tokens, it's the case that they both each can't be substituted for another one and they can't be divided, right?

And in the case of ERC-1155 semi-fungible tokens (SFTs), you can substitute them for others of the same type but they still each can't be divided. They're whole, irreducible units.

For both NFTs and SFTs, I think the non-divisibility is an important component to understanding what they are. There's no "smaller denomination" of each asset in the way that Ethereum can be divided arbitrarily until you reach the minimum "wei" unit.

You're right that non-divisibility isn't a sufficient condition to be non-fungible (as with SFTs), but the way I interpreted your first sentence made it seem like it was an orthogonal condition rather than a necessary and central one. (At least for cryptocurrency assets.)