is being a vegetarian more healthy?

heck no.

You don't need to eat foods from animals to have enough protein in your diet. Plant proteins alone can provide enough of the essential and non-essential amino acids, as long as sources of dietary protein are varied and caloric intake is high enough to meet energy needs. Whole grains, legumes, vegetables, seeds and nuts all contain both essential and non-essential amino acids. You don't need to consciously combine these foods within a given meal. Soy protein has been shown to be equal to proteins of animal origin. It can be your sole protein source if you choose.

Being vegetarian can be healthy or unhealthy, just as being omnivarian or pescatarian can be healthy or unhealthy. So long as you have a decent balance of whatever your diet requires (that is balance between protein, carbohydrates, vitamins, minerals etc.)