Welp, it's their opinion. But remember, PETA are a group with an agenda - the complete "emancipation" of all animals. It doesn't matter if Meat is good or bad, they are duty bound to condemn it.
Yes, excessive Red Meat intake does raise the risk of Cancer and Diabetes (type II) and obesity. I would also point out that eating too many french-fries (which are made with Potatoes), can also do the same. Eat too much of ANYTHING and it can cause obesity (fruit included!).
If you eat meat responsibly, as I do, you won't be overweight. I'm certainly not! I'm 5'7 and I weigh 64 kg, which is exactly what I should weigh according to the doctors. I have eaten meat my entire life - mostly lean meat, and mostly "white" meat like Chicken and Fish, but I do eat pork occasionally. I have also drunk milk my entire life. And I'm not obese or suffering from any diseases (that I'm aware of).
PETA are liars. They know this much themselves. Once again, their agenda isn't to tell the truth. Meat isn't perfectly healthy, but EVEN IF IT WAS, PETA would STILL say it was unhealthy, because they have an agenda to push above all else. They are opposed to meat eating and animal-product intake on a philosophical level and believe me they are willing to lie through their teeth in order to scare people. I don't trust a damn thing PETA say because they've lied in the past, and they'll lie in the future.
For example, PETA and many other Vegan societies keep on insisting that Milk is bad for kids. Thousands of years of human civilization, eating habits and decades of scientific research prove otherwise - that Milk, taken in moderation like anything else, is perfectly healthy and safe. People have been drinking milk since the time where we learned to domesticate animals - if it truly was "so evil" then we wouldn't have drunk it for THOUSANDS OF YEARS! Milk is nutritious, contains needed calcium and is great for infants.
But PETA hate Milk on PRINCIPLE. Hell, even if Milk extended the human life span by 100 years and gave people the ability to fly, PETA would still say "No, it's evil!". And the thing is, this propaganda does damage. In Asia, PETA propaganda and lies have turned large segments of the Asian Population against milk, claiming that it'll make your kids fat like US kids! Some asian relatives of mine have taken their kids off milk (their kids are 1 and 2 years old) because PETA have told them that their kids will turn into fat little white kids if they drink too much milk! No, I'm not joking. Not only is that propaganda racist against Whites and Asians, it hurts kids who need to put on as much Bone Mass Density as possible in order to decrease the likelihood of osteoporosis.
PETA care only about one thing - the elevation of animals to the same level as humans. Hell, they'd give animals the vote if they could. In Australia, they recently came out against the swatting of flies. Again, I'm not joking. That's right - they are against the killing of flies now. They are one step away from the lunatic brigade. What's next I wonder - opposing Mosquito clearing techniques in Africa because "Mossies have rights!". PETA claim they want "equailty", but I just seem them as a bunch of animal worshippers who think Bambi, with it's talking deer, was a documentary.