- healthy user bias: People who choose a plant-based diet (or in fact, probably just about any structured diet) are more likely to be health conscious in general and more likely to have other healthy habits like exercise.
- latent variables: "meat eaters" follow a wildly diverse group of diets, including those who eat just fresh lean meats, and those who eat heavily processed foods like bacon and sausage. Or those who eat just chicken. Or just fish, etc. A lot of the contradictory claims about "meat" seem to have a lot to do with these distinctions.
- self-reporting errors: Most observational nutritional studies rely on self-reporting of diet - there's a ton of research that shows that people regularly misreport what they eat in these studies (both qualitative & quantitative).
All of this is not to dismiss the results either - a lot of the time observational nutrition studies are the best we have! Doing randomized controlled trials on these kinds of interventions is difficult, so observational studies are often the best we can get, but they're really only a piece of the puzzle.