About what and why?
We can't comment much directly on Possessed's situation beyond extending our sympathy, for one thing it is his situation and he doesn't seem to be in full possession of the facts anyway.
Though sudden changes in personality frequently do have a medical explanation.
However in terms of the hypothetical situation of two adult parents having a disagreement. I can't see how anyone, even a child, could claim entitlement to private and possibly embarrassing information which may cause children (even adult children) to have chose a side. I can understand wanting to understand the situation but not the need to possibly irritate an already inflamed situation by forcing out information against the wishes of the parents.
Parents hold a position of responsibility for children up to an age so they are the gatekeepers of family information for small children. Once a child becomes an adult the relationship changes to one of more or less equals. In which case if you can have secrets they deserve that allowance of privacy also.
It's important to let both parents know that as a child you are supportive and concerned but to keep enough distance not to smother the situation and seem too intrusive.
That's my perspective.