Psychological compatibility
Psychological compatibility is a somewhat vague term that intuitively makes sense but has not been extensively researched. By psychological compatibility people usually mean the degree to which people inherently "fit" or "match" each other in interaction over a long period of time. Implied in the term is the idea that certain personal qualities influence the character of one's relationships, that these qualities differ from person to person, and that they are permanent. Most people would probably agree that such qualities must exist, but that they are very hard to put your finger on. In addition, most people would agree that there are a host of situational factors that influence relationship quality as well.
Part of the nature of psychological compatibility is that it is easier to recognize incompatibility than compatibility, since negative emotions are easier to recognize than the absence thereof. In addition, there are different varieties of incompatibility. In one situation you might feel repulsed by a person, in another you might feel strained and self-conscious, and in another you might have a sense of competition. Psychological compatibility probably applies almost equally to both same-sex and inter-sex relationships
In the absence of physical attraction, you would probably avoid building relationships with people you are incompatible with. Physical attraction can "override" and quelch feelings of incompatibility. This suggests that in humans the biological program of reproduction is more powerful than the psychological program of productivity, happiness, and self-realization. Perhaps, then, satisfaction of one's more basic needs leads to an increased focus on pursuing psychologically compatible relationships, in accordance with Maslow's hierarchy of needs.
Socionics and psychological compatibility
Socionics deals primarily with unchanging qualities of people - for example, the prevalence of one mode of thinking and behavior over another. Changes in people's attitudes and behavior can also be described in socionics terms, but they do not change a person's socionic type and, hence, their pattern of intertype relations with other types.
Socionics qualifies as a theory of psychological compatibility, though much work remains to be done to elaborate different varieties of relationships within a certain intertype relation and the causes of this variation.