Sometimes you make choices and sometimes choices make you.
I believe that this expression should be understood within the context of one's own choices, excluding the choices of others, so your interpretation that your parents' choice to perform horizontal gene recombination made you is not to be included as part of the discussion.
This expression is rooted in the idea that choices have consequences, and that some of those consequences are large enough to change your life. Indeed, there are times when we make choices, but there are also times that our previous choices change who or what we are without our volition.
To illustrate, consider the choice of experimenting with illegal drugs.
It is up to you whether or not you choose to start using illegal drugs. However, this choice will "make you" because in the future you could end up in jail ("make you into a criminal"), in rehab ("make you into an addict"), or worse, in a shallow grave ("make you into a casualty of a gang war"). You only chose to start using drugs, but you didn't choose to become any of the latter things (at least, not at the time you started using drugs), and yet your one choice led to you, that is your life, to being changed in some major way.
Of course, not all choices have such massively life-changing effects. Your choice of what cereal to eat probably won't affect your social status (it might lead to diabetes though :D).