The idea is that you want to avoid taking away the player's agency through purely narrative contrivance. You're trying to avoid saying, "Your character does THIS, because that's what I want to have happen for the plot."
That's why there's a difference between compelling a PC to do something through mundane persuasive pressure from an NPC, versus compelling a PC to do something through an established in-world mind-controlling power. The former is walking the border of narrative compulsion, whereas the latter is further away from that border.
Another big reason is that a lot of games have a very under-developed and unbalanced method of resolving basic persuasion, so that the target of it doesn't really have a fair way to defend itself. The game simply isn't designed for that to be a vector for the GM to attack the PCs with. For example, in Pathfinder, the only thing that helps against Diplomacy rolls is the target's base Charisma bonus. If I as the GM decided to build high diplomacy monsters to "diplomance" the PCs, they would be at my mercy. They probably couldn't come up with a reliable way to counter it even if they tried. Whereas there are lots of potential ways to defend against mind control spells.
Note, though, that there are some games in which it would be totally acceptable to compel PC actions through "words." For example, Burning Wheel has an elaborate system for verbal combat, called the Duel of Wits. In systems like that, persuasion is built to be a legitimate mechanical form of conflict. If you're playing a game like that, everybody can accept that there's a different social contract in play.
Hope that helps.
