People form a group where their likes dislikes match.
But Sometimes there meet people whose likes dislikes do not match but they have a level where their adjustment level, acceptance level match. There is a match of giving attention to each other's thoughts even when they do not agree. So, it's like you enjoy talking because of healthy input from both the sides. To me, this is compatibility.
Meeting with people who are compatible - is not very common. It may happen that the person you are staying with for many years is not compatible but the one whom you know just for few days/months might be really compatible. There is no limitation of duration for this. :)
Somehow I think, your love must also be someone who is compatible with you - who would respect your thoughts, who would give input of his thoughts equally, who 'might' oppose, might accept.
Compatibility, in other words, is to Help each other build up mature environment of acceptance.