Dairy from cows grazing on marginal land that is not otherwise suitable / efficient for other cultures is very competitive as far as producing proteins is concerned. Proteins are a necessary nutrient.
Industrial cattle fed corn is an entirely different story and should almost certainly be counted as a different category as far as climate impact is concerned.
Do you have a reference for this that tries to quantify the CO2/CH4 emissions per kg beef? For chicken, I've seen estimates of 3.3 kg CO2/kg of industrial chicken meat compared to 5.3 kg CO2/kg of organic chicken meat. Of course, from an animal welfare point of view, organic chicken is a lot better.
Carbon emissions from cattle comes from their feed. They're not fed petroleum. There is some incidental fossil fuel consumption involved particularly in producing industrial feed (corn), but that doesn't really apply for pasture-fed cattle. All that carbon was just captured by the grass or otherwise corn used to feed them.
CH4 is another issue, but again, unless I'm missing something, total CH4 from cattle in the atmosphere should be proportional to the average number of heads alive. If we don't increase herd size, it won't go up — unlike CO2 from fossil fuel use.
The bovid methane drumbeat is bandied by people who conveniently fail to account for the millions of missing American bison that used to produce comparable output.
Did they? Did anyone measure that? Or is that simply an assumption? Relatively small dietary changes can greatly reduce the amount of methane produced by cows (I believe you add something like 15% seaweed to the feed), so it's not at all clear that a free range bison would be similar.
Wild Bison aren't eating seaweed in the great plains. Cows in the plains spend their majority of their life eating the same grasses that the bison ate, then they spend a few months on a corn diet.
Industrial cattle fed corn is an entirely different story and should almost certainly be counted as a different category as far as climate impact is concerned.