I think the main problem with Friendship/Rivalry wasn't lack of understanding among the players, but among the writers. Every time friendship was used as approval and rivalry as disapproval, it undermines the system. Not just because it associates "rivalry" with "bad", but because it can make it hard to follow the rivalry path to the end if your character doesn't consistently act like a jerk.
Without meaning to sound condescending, but I'm inclined to believe the understanding is still lacking on your part. Or rather, I believe you are demanding/expecting it to be a direct replacement for the approval system functionally, which it is not, and are thus disappointed.
1) Not disagreeing with someone for a change, or disagreeing with a friend does earn you their occasional opposite inclination.
2) When it comes to gameplay and content: There is an option for each character's story which is sort of a breaking point, which will earn you almost maximum Rilvary and will constantly be referred to.
For example, if you decide to not give Merril the artifact. That is not acting like a jerk, that is taking a stand on your point. Also, if we're honest, those answers in which you would be simply acting like a jerk, a quite rare and seldomly highly "rewarded". Most characters only respond with approval at all when it comes to something that questions their beliefs.
At least this exemplifies why they did away with it, I suppose.
I didn't like it because it encouraged you to game the system regardless of what came naturally to you, because specific relationship events only happened with high friendship/rivalry. I would've preferred it if those relationship events were tied to specific choices you make regarding a character, or how you spoke to them at one or two key points, rather than how you accumulated points on a scale.
Iz is purely subjective, but that's actually what liked about it. If you don't interact with someone, they end up -genuinely- not caring about you. That's what not having high scores in any direction illustrated, and I think this hasn't been done for too long.
Choosing the right answer in certain situations is strange, because why would I even share anything personal with you, or confront you about something, if clearly we don't give a rat's behind about one another?