It all depends. What kind of meat? Turkey and chicken has lower fat and cholesterol that red meat (beef, pork). If you have high cholesterol it is probably wise not to eat fatty meals. Fish is high in omega three fatty acids (e.g. salmon), current claim is that omega three fatty acids are great for overall health. But disputes also exist...
Meat is simply mostly proteins. Your body (stomach) has to work hard to break down these proteins, which is good if you want to lose weight (e.g. compare to sweets or fats which are readily absorbed by your body without much effort). Meat, especially red one is great if you want to build and keep muscles. Other meat, such as turkey, contain tryptophan which is essential for production of serotonin, neurotransmitter in the brain associated with happiness.
Pure protein (meat) diet might be good for weight loss, the problem with high protein diet is that it is associated with Parkinson's disease.
People are foolish when they are trying to avoid fat and cholesterol by not eating meat. They think it will lower their overall cholesterol. The truth is, your body needs cholesterol to be healthy, it is an essential component, and if your body is deprived of it it will create its own anyway. You need cholesterol for example for healthy brain function and for testosterone (hormone). Basically you need some optimal levels, too little or too much of it is not good. Red meat also contains Vitamin B12 which can't be found in most vegetarian diets and needs to be supplemented.
Meat can be prepared in many different ways - cooked, fried, smoked, roasted, in oven or in direct fire... Usually you want to avoid any meal (not just meat) that is directly smoked, fried, prepared in high temperatures or in direct fire... These actually create a lot of carcinogens that are dangerous to human body. Best way is to cook/boil meals slowly and in lower temperatures for longer period of time. It is better to cook the meat than to consume it as raw. So you want cooked meals (not just meat), not fried, burnt or smoked.
You also want to avoid preservatives and processed meals overall; fresh is always better. Problem is also with "production", many times these animals (chicken, cows, pigs,...) are fed with hormones so they grow faster, and they are killed in highly stressful environment, which causes them to release additional hormones such as adrenalin and cortisol. The meat is then processed, added and presented to the consumers - who eats it with all these additional growth and stress hormones... Great, FDA approved - safe to consume.
Some fish can be full of mercury, which is a poison. You may not get poisoned by having a fish here and there, but if you eat it non-stop, year after year, it simply accumulates. But hey, as long as it is FDA approved...
Not to mentioned other foods, such as healthy vegetables. Many times they are spreyed with pesticides which is a poison that kills any living thing, and they are also fertilized by different chemicals which are also absorbed. As you know, chemicals are not good for your body. Let me guess - also approved by FDA?
Ok, lets don't even mention the chemicals in the air that you breath, chemicals released by factories into the rivers, chemicals that kills anything that lives in the water so you can safely drink it, chemicals that you use to wash your clothes in or brush your teeth with, chemicals that are added to foods to make them look fresh and colorful, chemicals that you swallow so you can be healthy again because they kill the bad bacteria in you, chemicals that you smoke...
Life is simply not healthy, but don't worry - eventually you'll get used to it
