I know I talk a lot about neutral game, but I think it's because it didn't truly click for me until recently, and from that perspective I can relate to where people are coming from.
As previously established, a lot of Smash players don't know what a neutral game really is. The reason why, is because they usually see the neutral game merely as a means to an end, rather than a game state in and of itself. Here's what I mean:
Sometimes I will see people say, "This character has a good neutral game, because they can combo off of a hit so well." Good combos aren't a good neutral: once you've hit the opponent, you're generally in an advantaged state. Good combos mean good advantages. Being able to land that FIRST hit to start the combo reliably, that's good neutral.
I will also see people remark that a character has a good neutral because they have an excellent punish game, which usually means converting an opponent's whiff or shielded attack or whatever into a long string of attacks for high damage. Again, the retaliation after a successful defensive maneuver isn't the neutral game. The chain of decisions that led you to picking the right defensive option and forcing your opponent to commit to an attack they didn't want - that's a neutral game.
I think misunderstanding this is what leads to some common odd ideas about characters in Smash 4. For example, I've seen people make comments like, "Marth has a bad neutral because he has no guaranteed followups" and because he can't short hop aerial. Conversely, I've seen people say that "Roy has good neutral becaus ehe has this throw combos."
The first step to helping people learn Smash 4 might just be to get them to wrap their heads around the fact that neutral is not just what happens in between combos.