So how am I wrong here?
I will give it a shot...
It is not really a question of you being right or wrong, it is more an issue of you just seeing the 'surface', and not the underneath workings.
'On the surface', you are correct in all of your statements/arguments, but 'on the surface' you are not accounting for the 'underneath workings' of how livestock are feed for market, and the greenhouse contributions caused indirectly from that process.
It takes considerable energy to plant, grow, harvest, process, and transport the 'plants' (think high protein 'plants' like grains (here in the USA, primarily corn) to the feed lots where thousands of animals are confined and force fed.
Do a little research on feedlots, and you will start seeing a bigger picture.
If the food animals were free roaming, and just eating what's naturally growing, you would be correct, but that's not the case.
There are a lot of other factors involved, but this should be enough to get you started.
I apologize for not explaining better, but best I could do this early in the day.
I hope this clears up your question.