It depends on how you look at it.
If we didn't meat, there would be a number of animals initially allowed to start prospering without us as predators.
The main one of those would be Cow, Pig, and Chicken. All of these animals would 1) eventually be seen as competition for our vegetation food, as their population would rise, we would kill them or drive them away.
Other predatory creatures like Wolves and critters that would thrive from eating chickens and such would begin to over populate. Most of these animals we see as a threat to ourselves. Any creature that can kill and eat a full grown cow, can also kill and eat a human.
So yes, we would have more predators as well, killing humans. Not that it would necessarily be a problem until the population of Cows pigs and chicken started to decrease, both from and excess of predators, and an increase in food resources based on the fact that we would demand most of those same resources leaving us as the only food source for the predators in question.
Therefore... we would in the short term of say 10 years or so Have an initial increase in population of cows pigs chickens with a simultaneous decrease in vegetation followed by an increase in predatory animals that would also have an effect on human population causing retaliation and extermination of those creatures ending in a kill or be killed scenario in which either humans or predators will lose.
Assuming we survive the increased population of predatory animals, we would eventually either resort back to eating meat or evolve (long term) into creatures that probably would not have incisor teeth, be leaner and smaller in build to accommodate for the lack of protein. If the battle with predators continues for long enough throughout the evolutionary period, the positioning of eyes on the future evolved us may be more on the sides of our head to create more peripheral vision, like that of prey animals.
Posted 1354 days ago