> In 2-3 trees, we split a 4-node into two 2-nodes. We can’t split a 3-node into two 2-nodes, though. Why not?

A 3-node cannot be split into 2-nodes because we cannot obey
the definition of a 2-node that it must have two children with the same height.
This is simply because a 3-node doesn't have sufficient children!

As a counter example, consider this non-leaf (or internal) 3-node:

 3,5
 /|\
2 4 6

which cannot be split into 2-nodes (3) and (5) because
there's no way for both of them to have two children each of same height!