Actually focusing on CO2, same site:

https://ourworldindata.org/ghg-emissions-by-sector

More than 70% of CO2 from energy, less than 6% from ALL livestock.

It's more than 6%. Cows eat a lot, so people cut forests to grow more feed (like in the Amazon). Deforestation contribute to global warming, not to mention the biodiversity damage.

Cows also eat lots of alfalfa and grasses which takes no artificial fertilizer or pesticides to grow. And produce a not insiginificant amount of premium quality fertilizer from it that is reducing artificial fertilizer production.

People don't need to eat beef from amazon.

If we care about deforestation then we definitive should also not use ethanol as a replacement fuel, since ethanol uses the exact same farming and plants as the one used for feeds. Animal feed and bio fuel farming are usually combined. The other main source of bio fuel is from the lumber industry.

How much more than 6 percent? Support your claim with reputable sources.

If your arguments aren't believable, I'm buying extra steak this evening.

flip the vertical order on that graph, its super misleading.