First of all i would like to Clear it that Islam tells us to do behave Animals With Mercy and Love and there are large number of rights given to Animals in Islam. If we read the Hadiths of Prophet Muhammad Saw About Treating the Animals we will find that no other Law or Religion Gives so much rights to Animal. Hadiths of Prophet Saw says don,t give pain to Animals, give them Proper food and don,t kill them uselessly. There is also a Hadith that a Women entered in Hell because she not given food to her Cat due to which the Cat was died. Now We Come towards why Islam Allows Us To Eat Non-Vegetarian Food? There are Several Reasons For this.
First Reason is that Animal's meat contains lot of protein that many Vegetables jointly cannot give to us. For example 8 essential amino acid exists in meat. Second reason is that God has given us such Omnivorous teeth that we can not only eat Vegetables but also meat. Now if we see Teeth of herbivorous animals like Horse and Goat their Teeth are Flat which cannot eat Meat. Now if we see teeth of carnivorous animals like Lion and Tiger we will find that their teeth are Pointed which can only eat meat and not Vegetables.
Now if we see Teeth of Humans they are Flat as well as Pointed due to which Humans can not only eat Vegetables but also Meat. Next Reason is digestive system of humans can eat Vegetables as well as Meat. next point is that Not only Islam but all other major religions like Hinduism and Christianity also allows to eat Meat in its Religious Scriptures. For Example Hindu Book Manu Smruti chapter 5 verse 39 and 40 says The God himself created sacrificial animals for sacrifice, therefore killing in a sacrifice is not killing. Vegetarians raises another point that Animals feels pain when we kill them so we should only eat Vegetarian Food. Answer to Such People is that According to Research of Modern Science Even Plants Feels Pain. When We Cut them they also feels pain so logic of such people of eating Plants but not meat proves wrong. The Last reason i would like to give is that if Every human on earth becomes a Vegetarian then there will be Over Population of Animals on the earth. So these are the Reasons that Islam allows us the eat Non-Vegetarian Food of those Animals that are Halal. May Allah Swt help us all to follow the path told by him.