If you eat meat you are indirectly responsible the death of a creature. Isn’t that breaking the first precept?
 
It is true that when you eat meat, you are indirectly and partially responsible for killing a creature but the same is true when you eat vegetables. The farmer has to spray his crop with insecticides and poisons so that the vegetables arrive on your dinner plates without holes in them. And once again, animals have been used to provide the leather for your belt or handbag, oil for the soap you use and a thousand other products as well. It is impossible to live without, in some way, being indirectly responsible for the death of some other beings. This is just another example of the First Noble Truth, ordinary existence is suffering and unsatisfactory. When you take the First Precept, you try to avoid being directly responsible for killing beings.