It's also quite difficult to explore opinions between two unrelated, insignificant characters. If one of the characters isn't directly ahead of the other in a hierarchy - as in a liege-vassal or head-of-religion relationship - you have to open a separate dialog. There are tons of distinct opinion modifiers, and I've frequently found that people plotting to kill random people have been tagged as 'rivals' for a mutual -100.
This modifier, like so many, is event based. There are many more events and many many more event triggers than opinion modifiers, so it's nigh impossible to tell with any certainty why an opinion modifier cropped up. As an example, when you take a pilgrimage, there is a small chance to cross the path of nearly any adult character in the game for a variety of different events; you could end up friends, or you could duel on the road and get a permanent opinion malus. What the event is, which options are available and which options the AI selects depend many inputs.
Aside from the sheer number of possible events, you as a player won't necessarily ever be eligible to see all the same events. Just playing as a ruler gives you different events from being a vassal. I also find I tend to groom my rulers to have high stewardship for large demense, so I usually only get one type 'high-stat' special option (e.g. you can diplomatically reject a lot of events if you have high diplomacy stat). I imagine that a lot of event special options for high intrigue or high martial characters are much less, shall we say, peaceful.
The rationality factor ties back into this, as Phillip points out. One thing to consider is that a seemingly rational person can end up plotting against a lunatic for a past transgression. Another common, but more obscured, give-away is if someone closely related to either target is a seducer (much more frequent with the Way of Life DLC), then both parties can get lots of events if the seduction target is in the same court or family.