I've only been in a relationship with an ENFP, which just based on type alone is not at all my opposite, but factoring in his enneagram(7w6) and instinctual variant(so/sx), it seems to be fairly safe to say we where opposites in that respect. He was extremely outgoing, whereas I used to be extremely introverted( I still am in that I enjoy spending/spend all of my time alone, but I know how to pretend to be an eSFP now when I need to.) He was very idealistic; I am fairly grounded. He was very enthusiastic and optimistic, I am much (MUCH) less enthusiastic and realistic(
pessimistic).
So in many ways; he was my opposite.
In regards to temperament theory though; he would be my opposite as SP and NF are opposites within that particular theory(at least that's what I read somewhere).
As for socionics; I am unsure as to what his type is, but I assume it to be something most definitely not Se valuing, I think it could very well be ENFp, as I could really see that. Although, the thing about that, that wouldn't make sense is that then he would have been my supervisor(if I'm remembering this correctly?) but I was clearly his.
As I've grown older, I notice myself being drawn to Te doms and auxes, it's very odd but I find their reasonable nature to be appealing as well as just finding them so freaking confusing. I've noticed from my interactions with a few ISTJ's in my life; that we mesh well together, like we fill in what the other sucks at. They're actually some of the very few people, I can honestly say I enjoy spending time with. I also like being the only person "like me" in a relationship, I would never want to date let alone marry myself.
As for my other opposite(shadow) ESFJ's, I seem to attract them as friends(well "friends", more like acquaintances)but I don't think I get along very well with them; mostly because I find Fe very scary.
So, tl;dr I am attracted to my opposites(uses same/almost same functions in different order) because I want to be the only me in a relationship and because they help me learn new things by/as well as filling in what I am not good at.