Becuause you are a puppet
Like so many characters in so many games, Kain is used like a tool. However, Kain has the misfortune of being used so many times that it almost seems like he has a split personality. He's under mind control for at least half the game, and it's impossible to ignore the consequences of his side-switching. The mind control problem never goes away, even when Kain regains full control of his actions. Unlike later Final Fantasy puppets- Terra, Cloud, and Rinoa, to name a few- Kain never gets over what he's done, and other characters have trouble trusting him. Edge certainly wants nothing to do with him. Only Rosa and Cecil continue to place their faith in him, but that says more for their inherent goodness than Kain's.
While under Golbez's control, Kain's personality changes. Everything he left unsaid and tried so hard to cover up comes to the surface. It's like that one episode of Buffy the Vampire Slayer when everyone's secrets come out in song and dance numbers, except with less music and spontaneous combustion. Still, it's embarrasing to have it all out in the open, especially for someone who is so proud and self-controlled.
The exact nature of the mind control in Final Fantasy IV is not made clear. It's obvious that people under Golbez/Zemus's control are evil when they normally wouldn't be. But the insults that Kain feels, the hatred of Cecil, that's not quite feigned. His jealousy was always there. How could it not be? But while Kain loves Cecil more than he hates him, under the influence the hatred takes over. It seems clear to me that sorcery makes the evil parts of mens souls grow stronger, and directs them to Zemus's purposes. It doesn't put evil where none existed before.
People often classify Kain as weak because he spends so much time as a pawn. This is both true and false. He is weak, in the sense that we are all weak, we can never manage to get all the sin out of our systems. Kain has buried his jealousy and ill-will for years under the surface. But what he buried will bury him. There's definitely a lesson about a festering wound and being honest with yourself that the game is trying to get through. There is a reason it's Kain under mind control. But could the story have happened another way? What if Cecil had wandered back to Baron. Could he have been the right hand man of Zemus? I think so, because the first half of the game is Cecil's quest to confront his inner darkness. He fights dark self and everything. Besides, Golbez says that it's easy for Zemus to control Lunarians. The point is, it's not just Kain who can be controlled. Yang was for a time. Edge's POWER OF ANGER could easily turn into the power of hate. It's a weakness, sure, but it's a universal one. Only Cecil, after he has claimed the mantle of Paladin, can use the crystal and defeat Zeromus. But as Zeromus says, even with the holy sword in his amorphus blob of a body, he can't really be killed.
One more thing. I've seen it suggested that Kain isn't really being controlled at all- that the "mind control" is just a convenient excuse. This idea is disproved everywhere in the canon, but it's interesting nonetheless. What if Kain betrays for his own reasons? He's no longer a good man in an impossible situation but a complex man willing to sacrifice his loyalties for power. But I still think his feelings regarding Rosa and Cecil are far from feigned.
Mind control is pretty weak as far as plot devices go- it was a while before the childhood best friends would begin to backstab on their own, but now they do it with alarming consistancy. Still, the idea of buried secrets and dark spaces coming out to haunt you is important to Final Fantasy IV. Mind control could be a fairy tale exaggeration, a metaphor for circumstance and necessity.