It’s a fundamental law of nature that one animal eats the other, and to do it as humanely as possible is not a paradox just a matter of rules since ancient times, i.e. kosher.
There are two things people are better not to know how these are made, sausage and law.
Sorry Professor Jac, "Strictly speaking, 'organic' refers to anything containing carbon." Carbon-dioxide, sure is not organic. Nor are silver cyanate and ammonium chloride. It was a milestone in science when Wöhler synthesized carbamide, aka uric acid, an organic molecle from those two inorganic ones.
Organic refers to life, i.e. organism. That's where the other use that you mentioned comes from. Organic farm product indeed means the made by organic, not synthetic substances.
RE: The meat paradox
Oh yes, the mind is wonderful. If only everybody had one.