I have had a recent on-line exchange with Nick Cooney on Quartz.

Me: "The health benefits of vegetarianism are often overstated. And there's a risk that, by promoting them, you convince people to cut out red meat but increase their consumption of chicken, eggs, and fish, thereby causing more harms to animals in the process."

Nick: "But there are still health benefits of vegetarianism. And, if you look at the studies that have been done, promoting the health benefits of vegetaranism reduces the number of factory farmed animals consumed (and that's true even for the people who just cut out red meat). Boom!"

Conclusions: Bear my points in mind — don't overstate the health case (which could make you look insincere), and watch out for people who replace red meat with chicken or fish — but in general promoting the health benefits of vegetarianism is a great thing to do.