Think about your favorite songs. I'd venture to guess that the reason you like them is not really the content of the song so much (although that is part of it), but the associations you have with them. A friend's recommendation, the first time you heard it, the general life context around when you heard it. It's not that the specific notes resonate with some inherent thing inside you, but rather that you decide you're going to like the song for whatever reason, and then you do.
Now think about your friends. There is certainly an element that you want to find certain people, people with certain characteristics, but really the reason your closest friends are your closest friends is largely because of the experiences you've had together.
I don't know what the exact fraction is, but it's certainly more "made" than "found."
Which leads to the question (of course this had to get back to technology at some point): why do online dating sites treat dating as a search problem? And if you were starting a new one, how could you get around that?
Here's an idea: you sign up on a site, they require a $100 deposit, then they assign you to do a certain (hopefully-fun) thing at a certain place/time. (with someone else, or with N other people.) If you don't show up, they keep your $100. So you show up, with the other people, and you all have an excuse to be there, and then you've started doing a thing with other people, which starts building these relationships.
It's like "forcing you to go on good dates" whether or not you have enough time, knowledge, or imagination to create good dates. (side note: coffee or food is generally not a good date.)
(also related: I've been reading So Good They Can't Ignore You. Your work is more made than found too.)