8 Primarchs turned traitors and joined Horus in his heresy against the Emperor and his crusade.
The simple, global reason is that they were closer to the Warmaster than the Emperor and when Horus turned against his father, they decide to join him out of loyalty. But I don't completely buy it. Sure, loyalty and trust in Horus is part of the explanation, but Primarchs are depicted as extremely intelligent, with a high sense of strategy, tactics and logistic, and couldn't ignore that a rebellion would lead to a violent civil war that turns brothers against brothers and turn the Imperium into a wasteland. But many of them joined Horus without a second thought and seems to have no problem with slaying other Space Marines during Isstvan events.
The reasons for the treasons of some Primarchs has been explicitly given in the lore. For example, Lorgar believed that mankind needs faith and was disappointed by the fact that the Emperor refused to be considered as a god. His bitterness grew after the events on Monarch. He instigated the Horus Heresy in the name of the Chaos Gods. Angron hated the Emperor since they met, and Alpharius/Omegon decided to join the Heresy to fulfill the plans of the Cabal.
On the other hand, I have no clue about Mortarion. I have not read The buried dagger yet so I don't know much about his personality, except that he is not of the fun and smiling type. He had the classic "Primarch upbringing": raised in a harsh environment and helped freeing people of his home planet before being found by the Emperor.
It seems that he had no hesitation in joining Horus but no reason is really stated in the novels I read so far. He was a strong opponent of the use of psykers in the legions so it is a bit strange to me that he decided to join the champion of the powers of the Warp in his heresy.
Why did Mortarion decided to betray the Imperium and join Horus?