The truth of the Forerunners uprising
So there's no definitive answer on why the Forerunners rose up against the Precursors, however I would like to try and put together a plausible theory based on the information we have been given. Now I understand that some of these accounts may be half-truths or misunderstandings, since the Primordial isn't the most trustworthy character and its viewpoint being skewed since it's not omnipotent and only has certain information and the Domain has been stated to rewrite its own information like actual memories while the Librarians viewing of the memories of the ancient Forerunners abandoned in Path Kethona may be skewed due to unknown information on their part.
But considering it's all we have, i'm going to give it a go:
The Precursors left evidence of there existence in the galaxy after seeding life and retreating to Path Kethona but left a few of there own behind to watch over there creations for one worthy enough to be given the Mantle. The Forerunners would eventually rise and begin to explore space and fine these remnants and the Mantle. They would claim it and police other species, which would draw the attention of the Precursors left in the galaxy to judge whether they were actually worthy of holding it. The Forerunners would be deemed unworthy and would eventually lash out and kill a few Precursors causing the Kethona Precursors to arrive in bulk to the galaxy to determine their fate. Eventually, the Forerunners would be chosen to be eradicated and the Mantle would be passed to their genetic cousins, Humanity should they pass some form of testing. The Forerunners would learn of this and in both jealousy and a need to protect themselves, strike back at their creators forcing the survivors to flee to Path Kethona while some flee to Netherop.
Obviously this isn't canon but it's the best with what I could given what we know.