I just had to reply, I was so stunned to see this subject line in the list of 'new posts,' because this is the topic of my local poly meet tomorrow!
I think perhaps my realization was not all that sudden. I read Stranger In A Strange Land (Heinlein) when I was very young (10?). It was extremely important to my parents, that book. Mostly my dad. Just a small part of that is multiple loving relationships, but it is presented as the most ordinary thing ever. Or at least that was my impression. I didn't know anything about intimate relationships, save what I saw in my folks. (which is another post)
I was a little surprised, my senior year in high school, to discover I was attracted to women (I'd been 'boy crazy' since I was five). I read some articles about gays in the papers, and I was all 'women are an option? srsly?'
Just a few years after that, a woman tried to start something with me, while she knew I was living with my girlfriend. Eventually, I found out she had been trying to start something with my girlfriend as well. We attempted, for like one minute, something like a triad. GF and I had zero reference or experience of knowledge of anyone else doing such a thing. Lots of girl drama ensued. My issues were with being excluded. I'm not sure what their issues were. (this was thirty years ago!)
Being bi, I did dream that a couple might be the perfect thing, but I wasn't going to hunt for it. Once, while leaving a bar (at closing) a couple propositioned me, and it was so slimy, it put me off severely. I always figured that if it happened, it would be organic.
And then it was. My story is also in my blog, but I guess it doesn't pertain much to your question.
Although, I will say, I have not felt the need to seek counseling for the poly. I have been in and out of one sort of therapy or another for most of my life. I'm lots better for it. I have therapy to work on myself, or even on what I bring to relationship. But I don't feel specifically weird for the poly aspect.
I also go with the definition of poly (for me) as I'm capable of being in love with more than one. Just like bi is I'm capable of loving men and women, but bi doesn't mean I require both. So far, I haven't required more than one partner; but that might be changing. My current partner is an extreme introvert, and I suspect I might seek out another. Too early to tell.