Whether two things can work together without harm. Compatibility is a property of the pair, never of either alone.
Medieval Latin compatibilis (able to coexist), from Latin com- (together) + pati (to suffer, endure, tolerate); whether two things can bear existing together without harm.
Latin pati is to endure, and compatibility's root is tolerance shared, not sameness — two things compatible are two things that can each bear the other's presence. Neither one carries that property alone; it belongs only to the pairing.