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When trying to convince others you will quickly run into science. Without being able to understand scientific literature, how can you fight back?

https://en.wikipedia.org/wiki/Epidemiology

https://en.wikipedia.org/wiki/Longitudinal_study

https://explorable.com/scientific-observation
https://explorable.com/cause-and-effect

First you have to understand the limits of observational studies. The best they can do is prove correlation and causal inference. Its easy to be like "look I found a peer reviewed scholarly journal this proves it!" or "look here's one thousand testimonials I can't be wrong."

You need experimental studies to prove causation. The problem with experiments dealing with health and people is you can't be like eat red meat for 10 years then eat vegan for 10 years. For starers people wouldn't comply and secondly it might be immoral.

     For a controlled experiment mice and rats after often used. The problem of course for a vegan is that many are animal rights activists. Proving vegan is the best diet is going to be very hard if not impossible without using animals.

    Why, because observational and cohort studies can at most prove causal inference meaning red meat may cause diabetes, cancer, etc. Without an experiment there is no way to prove causality. That being said if your trying to convince someone else using scholarly peer reviewed sources and the scientific method, stop looking at observational studies.