I know absolutely zero couples who got together because they met at a bar or club. I'm like you - came from a very nerdy, educated, ambitious group of people. The folks I know who go to bars or clubs regularly are in the low single digits. (I'm struggling to think of more than one, actually, and this includes my Facebook regulars...)
Here's the list of "how we met" stories among my friends/relatives that I'm aware of:
- School - my cousin and his wife were in the same circle of friends in college, and I have a number of friends who met their spouses in college or grad school. My old roommate met her husband at an extended education class for teachers.
- Proximity - a college friend met her HS sweetheart-now husband when they worked at neighboring stores in the local mall
- Social clubs - friend met her husband in taekwondo, another met her bf through extended social circles from shotokan karate, my sister meets guys to date through lindy hop/swing dancing, my cousin met her husband doing swing dancing as well
- Social outings related to interests - friend met her longtime bf at a mixer for writers at a comic book store
- Online - myself and a few other friends. Some from online dating, others through not-romantically-inclined online communities
Given your personal interests and preferences for socializing, perhaps there's something from that list that will suit you?
For me, I'm an introverted hermit who's incapable of being flirty or sexy, so online was pretty much it for me. (I'm friends with a lot of guys, but they all think of me as a little sister or a fellow bro.

)
Despite being a woman (which is supposed to be easier, I suppose for the hot ones it is), it took me 2.5 years to find my first bf there, and that was checking on it every 2 weeks or so. (It was mostly luck that he became my husband!) Stuff like that can take time, even if it eventually works.
Your friend and your dad are correct in that it's something you can't really force. Having "a relationship, any relationship compatibility be damned" isn't a goal that none of us here are striving for, I don't think. But it is something you can work toward - joining clubs, trying online dating, that sort of thing. In order to meeting that special someone, you really do have to put yourself out there to meet people, even if it's online. You can't be sitting on your ass wishing someone would just magically find you.
At the same time, I think that having a "friends of the opposite sex" quota is needless and perhaps a little treacherous, depending on your motives. My husband is an excellent equal partner and very much a feminist (albeit an unknowing one - he was raised by a strong independent mother so it's what he knows), and he has ZERO female friends. He simply never found himself in social situations where there were women. Yet he treats me as a complete equal, doesn't treat women as a commodity. He treats me as a person.
So that's really the long and short of it. Treat women as just like we're people, because we are. Maybe don't treat us
exactly like your fellow bros, but it's not like we need any sort of "special treatment" or anything.
That's what I notice about guys who have a lot of female friends. It's not like they have any special insight into "how women think." They treat their female friends just like any other friend - they don't have ulterior motives about getting into anyone's pants, they don't panic about what to say or what not to say around them. Everyone's the same. And that's what women want, most of all. To be treated like any other person.