I think a lot of this kind of vegetarianism argument relies on humans' tendency to grossly overestimate in certain situations. Numbers like 0.05 seem like nice sensible small numbers. They feel reasonable. Few people when thinking "maybe this has a small ratio" will spontaneously pick 0.000000001. That feels like too small a number and if you're even thinking about something you feel it should have some value higher than that.

Then the vegetarian calculates using the overestimate and concludes eating animals is horrific.

The Drake Equation does something similar for calculating how many extraterrestrial civilizations there might be.