Humans were not designed to eat meat, but we can after some unnatural processing. Vegetarian/Vegan diets are healthier because of our body design in relation to food. Like you mentioned, human intestines, like herbivore intestines, are longer to digest plants. Carnivores have shorter intestines so that the meat does not stay in the body too long and start to poison it as it rots. The canine teeth in humans are very misleading. Look at a gorilla. They have very large canines despite being vegetarian animals. These teeth are better suited to bite into fruits and plants than animals. In fact, carnivores have claws that they use to hunt which are vital in catching prey. In addition, carnivores have very few molar teeth if any. Animals like horses and humans, have many flat teeth intended for grinding plants. Carnivores swallow more than chew meat. They need the canine teeth to tear meat, not chew it.
Humans don't tear meat. They first cook it (no other animals does this to food, therefore unnatural) then they cut it with an tool like a knife (there goes your whole canine theory) then they chew the meat, not swallow it whole. Then the meat stays in the intestines too long for it to be healthy. That why vegetarian people have a significantly reduced risk of cancers related to the colon.
There is nothing really natural about eating meat. Yes, we can, but our bodies are probably not intended to do so. If you add all the evolutionary evidence and science around the issue, you will start to see that humans are not intended to eat meat like we do. Vegetarianism is healthier and makes more sense regarding our body design.