it's not just cows grazing on grass--78% of cows in the us are factory farmed, and 97% are grain fed which means they're force fed cheap grain to fatten them up for slaughter. Moreover, only 3% of cattle can be considered grass fed, and, for those cattle, we're deforesting the amazon rainforest--so probably more than your 12 mice.
If you want to throw global warming on top of it, your lifestyle will contribute to the mass Exodus (and most likely death) of millions to billions from the global south.
It's kinda ironic you said I'm arguing from emotion, but all it took for you to be complicit in rape, torture, and slaughter is a smiling cow on the side of a fucking cheese package.