I'll start this right off by saying that I'm sort of cheating, since I chose ambidexterity rather than actually switching to my left hand, but I figure it still counds as the counterpart to bisexuality rather than homosexuality.
In any case, I don't remember how old I was when I made the decision -- most of my childhood memories can only be dated by pinning them down with a piece of then-new pop culture connected to the memory in question -- but my best guess is around ten. I do distinctly recall where I was, though; I was sitting in the backseat of our family car, a rather nondescript early-2000s Mazda Protegé, and on the sketchpad (technically a clipboard with blank paper clipped to it, but same idea) I carried everywhere, I wrote the alphabet -- both uppercase and lowercase -- in the shaky, wobbly printing of a child half my age or less and doodled a few simple pictures with my left hand.
Although I swiftly grew bored of doing so with any kind of dedication, the beauty of the idea of training myself to be ambidextrous is that it's not something that needs a lot of time or effort. All I had to do was, whenever I noticed that it was handedness-dependent and it wouldn't cause much of a setback to do so, switch tasks I typically performed with my right hand to my left hand, or alternate hands for those that required both: eating with cutlery, opening doors, use of a mouse, wiping with toilet paper, the list goes on. After all, it seemed to me more a matter of building manual dexterity and getting accustomed to my hands being interchangeable than any inherent property of my right hand.
Why would I do such a thing? Well, at the time, I don't actually think I had any reason besides "why not". However, the most practical justification I can come up with is that, in the event that I lose the use of my dominant hand (either temporarily or permanently) for some reason, it would be tremendously useful to be ready to go with my left; being capable of performing any manual task with either hand also adds more flexibility to my life even outside of such a scenario. I don't really have the coordination to do so yet, but being able to do two one-handed tasks at the same time would be useful as well. And, finally, getting into the realm of more emotionally-based reasoning, I'm a lifelong xenophile and thus find doing things left-handed to be kind of neat.