Time travel error

I love the Sands of Time trilogy, so i'm not bashing the game at all, but it seems odd that they would have the Prince able to change his fate, it doesn't make sense.

He saw the Sandwraith get killed by the Dahaka, therefore there is no way that he can change that. It's already happened. When he becomes he Sandwraith and allows his past self to get killed instead of him that shouldn't happen. It's not something that can be changed.

And even if it is, the fact that his past self died means he no longer exists in the present as the Sandwraith, because he is dead and so can not go back and become the Sandwraith in the first place.