First, consider your sources. Veg and veganism are borne mainly out of moral subjectivity and unsubstantiated silliness. They pretty much get it all wrong, but the things they get right are more a coincidence than anything. Solely by forcing people to eat more micronutrients and fiber and fewer calories, those diets by default can improve health beyond the average diet because the average diet is garbage

If you actually want to do it right, look at the biology. This will show you that cutting out meat isn't actually beneficial, but cutting out grains and dairy generally is. Eat that which our species evolved for, not what hippies say. We evolved for a wide array of fruits, vegetables, nuts, and meat; grain and dairy were introduced very late in the game, and have been quite problematic since.

Better yet, do some research and know what you're doing. It's not the hardest thing in the world. In fact, cutting out meat product is extremely unhealthy (things like lack of dha/epa, but lots more stuff too). There's a reason we've been eating what we've eaten since the dawn of man