I'm from a similar situation as the OP, in that neither of my parents were "car people", per se. I would say they can both appreciate good cars, but my uncle who lives 500 miles away and I'm lucky to see once a year is the only other true "car guy" in the family.
So where it came from is beyond me, but there is no doubt the attraction for me is there at the most basic level. It's innate, coded into my DNA, and present from birth. As a kid it was tractors, trains, and construction vehicles that the obsession was directed towards. By age 5, at any farm or highway construction site I passed I could name every vehicle present, what its function was, and how it performed it. At about 9 or 10 I picked up my first issue of Motor Trend from the school library (I can still remember the cover vividly, there was a red Lingenfelter tuned C5 'Vette they had clocked at 226 mph during their test) and it was all downhill from there. Motorcycles then came into the picture somewhere later in my teens.
As to what it is about cars that I enjoy, that's a hard one to answer as well, but I do think I enjoy wrenching and driving in equal parts. I like my daily commute, road trips, back road blasts, pointless Sunday drives, towing or hauling heavy loads, winter driving, hopefully I'll be giving wheelin' a shot soon, auto x, and one day I WILL get my ass on a track. Its all enjoyable in different ways. Wheel-to-wheel racing on a track is one of penultimate life goals, as it feeds both my competitive drive as well as the car passion. I love auto x, but I have to imagine it is basically like methadone by comparison.
The satisfaction from doing a job myself is also immense, taking something and making it better or making it my own. I constantly am on the look out for new noises or vibrations, to the point of being an automotive hypochondriac. I'm 100% a form follows function type guy too, but if I can make something pretty as well as functional all the better. That being said, I absolutely loathe any sort of detailing work and view even washing or waxing as a major chore, which is why my cars are always dirty. Hell, I don't think I have ever washed my current bike. Car shows don't do a whole lot either, not enough "action", but I do enjoy seeing other people's craftsmanship and approach to solving problems. I DO however enjoy restoration work, making a crap bucket nice again, and the "rattlecan resto" I did on my '72 Honda CL175 was one of my favorite projects to date.
My taste in cars is so completely eclectic that I really cannot explain it - I like Euro stuff a lot, muscle cars, offroad rigs, pure racecars, hot rods, luxo barges... I just happen to be on a bit of a "Buy American" kick at the moment, with my Camaro and XJ, but I think I defy classification into typical "car guy categories", as many of you probably do as well. I think that's a lot of what draws me to the GRM community, because everyone else here seems to be the same way, or at least gets it.
So I don't really understand where this car thing came from or what draws me to it, but I know I need it. Its what led me to study engineering, what gets me out of bed in the morning, what compels me to earn a paycheck, and what I think about nearly 100% of the time. In the end, I don't think I really care to understand it as long as it continues to keep me happy and give me fulfillment in life.