(He got it completely wrong, incidentally. He thouht I was aiming for a metaphor about science gone mad; I was trying to say don't neglect your pets because it'll come back to bite you in the ass.)
I don't mean to sound negative, but if it were me, I would let the guy think it was about the fallacies of science before telling him it was a PETA ad. Just saying.
You shouldn't be getting worked up just because somebody interprets your piece a different way. That's the point. Bertolt Brecht wrote in such a way that different people who watch or read his plays would disagree as to the argument contained within. Robert Wilson refuses to explain anything he does, and it is entirely up to the audience of his works to interpret what they will.
Similarly, allowing yourself to get too narrowly focused on what you want your work to be is not beneficial. Let these interpretations flow, and if you like them, weave them into your writing. People don't interpret things by accident: you had to have actually done something to make them think of this. In February, two of us performed a work of physical theatre (and I know that you're not referring to acting, but this same principle applies to writing. I've done both) in which we represented crops growing in a field, entwining together, and finally being harvested before growing anew. One interpretation we received of an erotic message, another involved the desperation of relationships. Neither of these was what we actually had in mind, but they were interesting avenues to explore nonetheless.
At any rate, it's your responsibility as the writer to communicate your message. Making the choice to disguise it is up to you, but if somebody else interprets it a different way, it is simply what they experienced from your work. Which is to say, it's your own fault.