It seems to me that some of the conventions for determining compatibility could be a bit outdated. In this post I am going to focus on person A's planet in trine to person B's planet, and this being interpreted as great for compatibility.
Like does attract like, but opposites attract and dissimilar traits complement each other. What "is" goes towards what "isn't". People seek traits in others that they don't have or can't use well. Some astrologers even think that "bad" transits are really just our subconscious manifesting what skills and traits we need to learn/practice in the outside world through people or situations.
It is likely that when people with very similar traits first meet, they are excited/comforted at first but then get tired of it; it wears on them being close to/around someone that is just like them. No one really loves themselves that much except narcissists. An echo chamber is fine for awhile but it gets to be boring and limiting. That is why many astrologers say trines are really a disadvantage and that squares are advantages--for the "learning" reasons stated above.
It is true, for example, that all the fixed signs don't get along but that is not because of fire and earth (or air and water) being incompatible. It's because they are the same temperament (fixed/mutable/cardinal). If two planets of the same type are in contact regularly, they will eventually get tired of competing with each other because no one will "give". They often don't accept each other's point of view or feel fulfilled. The easiest relationships have a "give and take" or "push and pull" element to them.
In this example, most would tell a Leo and an Aries to go for it because they are in trine, but would tell a Leo and a Cancer to "try really hard and maybe it'll work out." I disagree--Cancer likes to be Mommy and Leo likes to be the Child. They seem to compliment each other well. It can fall apart if Cancer never gets appreciated for all the attention they lavish on Leo, but can you imagine two fire signs working out any better? Aries is too independent to worship Leo all day, and when they do "play" together chaos ensues (like two crack fiends at a party). A Sagittarius' far visions are accepted and encouraged by Pisces, who likes to share their own dreams. These two benevolent people could use Sagittarius' drive and Pisces' compassion to change the world for the better. A Cancer and a Pisces? What a mope-fest!
