Of course vegetarians can be healthy. Most are not, because their dietary choices are so poor. Does that mean that any meat-eater is automatically in good health?
Probably not. Most meat-eaters are not healthy, because their dietary choices are so poor.
The key is to make good dietary choices, and have the widest possible variety of foods given your choices (vegetarianism, vegan, etc) or culture (hard to eat dog in Australia, and not much beef in India). Most people
in the West are eating crap. Whether that crap happens to have meat in it or not makes little difference.
Fruit, vegetables, nuts, beans, grains and tubers - these can provide all the nutrients a person requires. Likewise, meat and fish can, too. But any time you cut certain food types out of your diet, it's going to be harder for you to get the right nutrition, you're going to have to think about things more and plan a bit.
Bill Pearl became a vegetarian at age 39. It does not appear to have made him waste away into nothing.
It is true that many vegetarians are scrawny and weak. But it is also true that most meat-eaters are obese and weak. The simple fact is that most people have no clue what good food is, whether it has meat in it or not.
Learning about nutrition and cooking your own food are good things. It'll save you money and improve your health. Eat the widest variety of food your choices or culture allow, and if you can read, you can cook, and should cook.