No we do not. "What is human" is being a member of the human (animal) species. It's as easy as defining what is any other animal species.
Not everyone things it necessary to search for any additional justifications to treat our own species differently from any others. That it is our species is enough.
How we differentiate ourselves from other animals has been a moving target for many years: language, tool making, laughter, self awareness (using different definitions) have all been used. tool making was the dividing line when I was growing up. You may feel that our "species label" is sufficient to separate us from the animals, but for the most part people do not feel that way. We keep looking for reasons that our species is somehow "better than" or "sufficiently different from" all other animals. We apparently do not like to think of ourselves as merely an extension of an evolutionary process.
Still, the obvious test is: other species can have "rights" if they can demand rights, communicating and arguing for that demand. None other in the planet can, therefore we humans treat them as objects. Because they cannot communicate effectively with us, we cannot really treat the any other way. Even those who want to grant them "rights" are treating them as objects to be manipulated according to the will of humans. They only disagree as to what they will for those other animals.
Humans the only animals that laugh! No.
Humans, the only tool making animals! No.
Humans, the only animals that use language! No.
Humans, the only animals that are self aware! No.
Humans, the only animal who can demand rights! Well, yes.
But, you might as well add "playing the trombone, flying airplanes and taking pills for ED" to your "demanding rights."
You have sought out that differentiation in the same way by declaring that "no critter gets rights unless they ask for them," and claiming that human standards are the only standards that count. The same kind of thinking led to the worse abuses of European colonialism when they met "non European species" of humans for the first time. I think, for the most part, we have moved away from such ideas and it has been to our credit and benefit. The next barrier is thinking like yours that say, "If the can't hire a lawyer to file a suit, then they don't deserve to live." Therefore animals should be exploited.
It is not really about rights; it is about respect. It is just that our system only respects that which has been adjudicated by the courts. We demand that the courts tell us who and what to respect. We needed the Civil Rights Act of 1964 to tell us that segregation was wrong. That law was passed because white people insisted it be passed. Black people had struggled for a hundred years and they couldn't do it on their own. People have to act on behalf of animals just because there are people like you who refuse to accept their value unless a court says they must.
Those who really understand evolution realize that it is a seamless weave of all life and for the moment humans are the current front runner. We are paying a high price for our lack of respect for the rest of life.