Companionship or Compatibility?

I have recently begun to wonder which is more important:
Companionship or Compatibility. When our search for another person is driven enough, what are we willing to sacrifice within ourselves in order to achieve a compatible healthy relationship? There is a certain amount of give and take to any coexistence between two people. One might ignore an annoying trait within a partner because, on the whole, the partner is a good fit, so to speak. But when does it become too much. When do we start to ignore large glaring, perhaps negative, personality traits for the sake of companionship?

The world, or rather society, teaches us that it is good to be self reliant, self sufficient, self sustaining...Without need of another person. I feel this view is unrealistic and unkind. Though no person should be completely reliant on another (excluding children, people with mental incapacity, etc.) it should be a normal feeling to want to share the everyday mundane with another person. This need to be completely unneeding of any other entity is unnatural. Most cultures throughout history have acknowledged the need for human companionship in one form or another. People grouped together in tribes, villages, communes, even cults in order to maintain human contact. Those who were outcast or chose isolation in one form or another, often had emotional and mental repercussions.

Perhaps it is Valentines Day that makes me think this way. Singlehood looming over many of us makes this holiday feel like a farce and a depressing tradition. How do those of us that are not connected with a companion deal with the world at large on days such as these? Days that put into keen focus the dichotomy that society pushes on all of us. Be self reliant but not alone.
This in itself has made me realize that to be human is to want a companion. But while I may want a companion I have realized I am not willing to give up on the ideal of compatibility. I deserve, we all deserve, to be accepted for who we are and to have a person that we accept whole heartedly. The need to have a companion should not outweigh the need for compatibility within a companion.