The notion that only humans have rights-- because they are human-- is called speciesism, which is a kind of prejudice like racism and sexism are kinds of prejudice. You can't say that humans deserve rights just because they're human any more than you can say that males deserve rights just because they're male. Biological differences are NOT relevant to the question of moral rights.
Animals have rights for the same reason that babies and people who are mentally handicapped have rights.
As Tom Regan says in his book "Empty Cages"- we are all "subjects of a life."
"...we are like one another in relevant ways...Not only are we all in the world, we all are aware of the world and aware as well of what happens to us. Moreover, what happens to us--whether to our bodies, or our freedom, or our lives themselves--matters to us because it makes a difference to the quality and duration of our lives, as experienced by us, whether anybody else cares about this or not. Whatever our differences, these are our fundamental similarities."
Gayle