Much has been said and written about the quest for completeness in human beings and thus the attraction towards the opposite. What we term as attraction is actually "completeness being sought." This completeness can't be attained by merging the opposites but by merging things that complement each other.
Take example of two opposite poles of a magnet. What the north pole possesses isn't available to the south pole and what the north pole lacks can only be fulfilled by the south pole. Thus, they get attracted and combine to manifest unity.
Look into another example of two oppositely charged particles. Both positive and negative particles actually seek "completeness" which makes them come close to each other and thus unite. Positive and negative charged particles are not opposites [They don't cancel each other. "Light" and "dark" are real opposites.] Charged particles complement each other to form unity. Everything in this universe is in search for its missing parts.
What makes Na (sodium) react with Cl (chlorine)? If you remember lessons from your high school chemistry, sodium has 1 electron in its outermost shell while chlorine has 7. Sodium can "complete" its outermost shell by losing one electron (where completeness is defined as having the last shell 2 or 8 electrons) and chlorine can "complete" its outermost shell by gaining an electron. Thus, its the universal quest for completeness that makes them have an attraction towards each other and hence combine to form sodium cholride (table salt).
And based on my experience I would say that people who are almost alike in personalities can never constitute a good friendship; there is usually a teacher-student relationship in these cases or worse: there is professional jealousy in these cases. So even our friendship is a manifestation of a lost part of our-self. And this brings me to a very perplexing question: "Where exactly do I end and where exactly do you, my friend, begin?"