The most basic problem with animal rights activism is that it is simply not workable. It is not a livable philosophy. If people who advocate for animal rights were to achieve their goal of imposing their ideas on the rest of us, then life as we know it would become dysfunctional. Consider the following points. Leather is a made from animal skins. A great deal of our clothing is made up of animal furs. Tires, shampoos, and toothpastes also contain animal ingredients. Thus, taking up an animal rights activist mindset would require us to make numerous modifications to fundamental aspects of our lives.
If we endorse animal rights activism, then what are we to do with all the carnivorous animals? If we are mere animals, then what objective basis would there be for us to not eat meat? If we were to join the animal rights movement, then why not also establish a plant rights activist movement? If animals are to be treated in the same manner as humans, then they also need to be held to our standards of punishment when caught misbehaving (which would cause them pain and suffering). It is also ironic to note that many animal rights activists are supportive of abortion.
So, how are we supposed to treat animals? The answer to that question depends on the moral principles we hold. Ethics always begins with an objective standard. Mankind was created in the image and likeness of God (Genesis 1:26-27). This is why Scripture prescribes the death penalty for murder. But the eating of plants and animals has been permitted by God. We have been called to exercise good stewardship over His creation, which includes animals. Animals are not to be killed to the point of extinction or for our own enjoyment. Animals are not to be treated cruelly. Animals cannot have rights because they are unable to make free choices and act with moral accountability.