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"Livestock pollutes more than all cars, planes and ships combined."
They make claims about the body or nutrition that the evidence does not support. When they fall, they take the speaker's credibility with them.
Why it is weak
The phrase comes from the 2006 FAO report, which compared livestock's 18% of emissions with about 13% for transport. But the accounting differed: for livestock it counted the whole chain, from feed to slaughter; for transport, only fuel combustion. One of the authors acknowledged the problem in 2010.
Repeating the comparison gives the other person an easy rebuttal, and the discussion becomes about the number.
How to say it better
Use comparable figures: livestock accounts for between 12% and 14.5% of human emissions, according to the FAO, and animal-based foods for about 57% of food production emissions. That is already a lot, without a mistaken comparison.