You confuse logic with morality. You can'y apply logic to come to a moral conclusion, you can only use logic to justify your moral beliefs.
That's idiotic. Why wouldn't you be able to apply logic to come to a moral conclusion? Identify your base assumptions and your goals and work from there like any other conclusions.
Quite simply, morality is too opinionated. In order to see anything from an angle of right or wrong, you must discard that which makes it right or that which makes it wrong.
Otherwise, something simply is what it is, with qualities it has. Killing animals is killing animals, which is then used for food, clothes, and various other materials.
Animals feel pain, this is fact. Is that a moral dilemma? To expand on such, animals will always feel pain. Also, most things meet a gruesome end, and is almost always used as a recourse by another animal after death.
This seems fairly logical, still, this goes with the ideology that I have already decided that eating meat is okay.
Reversely, I could say, Animals feel pain, but we don't need to make it worse. Animals are living beings and should be preserved. If they must die, it should only be when absolutely necessary and despite animals killing others being the natural process, humans have gone against that process many times, and we should do so again.
Both of these statements are logical, but are completely contradictory.
For me, it comes to a point where you must simply accept that things suffer, and move on.