What do we gain by respecting the rights of other
animals if they do not respect our rights?
There are some wild animals who respect the rights of humans,
such as dolphins who help drowning sailors swim to shore. There
are also countless examples of domesticated animals, such as
dogs, who risk their lives to save their adopted human family,
even though they were never trained or instructed to do so.
However, it is true that for the most part, these are the
exceptions rather than the rule.
In many cases, we can choose to violate the rights of other animals without ever having to suffer any consequences. We do not have to fear a punishment for this in an afterlife, and the animals will never be in a position to exact retribution. So from purely the perspective of self interest, in many cases we have nothing at all to gain by respecting the rights of animals. Most animals are simply not capable of returning the favor.
However, morality is not about trying to figure out how to maximize our own selfish interests. True morality is not displayed by a shrewd politician who acts benevolently only because the TV cameras are watching. Nor is it displayed by someone who is kind to others only because he expects a favor in return. Nor is it displayed by someone who behaves a certain way only to avoid punishment in an afterlife.
In my opinion, true morality is about acting in the interest of others, even when we have nothing to gain in return. We often make sacrifices on behalf of those who will never make a similar sacrifice for us, and on behalf of those who we do not even know. This is what we do when we donate money to organizations like UNICEF (United Nations Children's Fund) which help alleviate global poverty. We do this not because we expect to be paid back or because we expect to be rewarded in an afterlife. On the contrary, we do it simply because we believe it is the right thing to do.
The same is true regarding the question of why we should respect the rights of other animals.
Follow up questions:
Why do we have a moral obligation to animals who do not understand moral concepts?
Why should we behave better towards animals than they do towards each other?
What is meant by the term rights?