The first and foremost principle of yoga philosophy is AHIMSA meaning NON-VIOLENCE.
It means not harming / hurting others and yourself physically, verbally and mentally. If you tend to injure yourself by pushing harder during a yoga practise, even that is considered violence against yourself.
When you take the NON-VIOLENCE to the next level, then it means not to hurt the animals and other living beings. Yoga is a way of life and it embraces PEACE. Love humans and animals alike, every living being has the right to live.
You can't impose vegetarianism on others as that kinda of action will be considered HIMSA (Violence). Becoming a Vegetarian should be a conscious decision taken by the individual as he progresses in his Yoga journey.