"inalienable human rights" and/or "god-given rights" depend upon the society in which you live and are therefore, in my opinion, social constructs, just as Mr.D said...
in a social and legal sense, I think we all do have a right to at least exist; however, I see this as more of an evolutionary response to the basic need to ensure the continued survival of the species, as well as a way to coexist when there are so many of us in such a small area...
for example, you can't kill another person because it takes too long to replace them (35% miscarriage rate among females of our species, a long gestation period, 18+ years and a couple million dollars before they're viable and useful to the rest of the species, etc) in comparison to other species, such as a lion or a chimpanzee (kill a female chimp/lion's offspring, she will go into heat within a matter of weeks, leaving her available to bear the young of a new male...and females of many species can have more than one offspring in a year)...I'd go into some of the other "rights" we have, but then this would get too long...
long argument short, I think we should respect each other and leave everybody else alone as much as we can, but I don't think that just because we were born of the human species that we are somehow entitled to better treatment than the rest of the multitude of creatures that inhabit the planet
a little off topic...one thing I think is interesting is that the American belief that we have the right to "life, liberty and the pursuit of happiness" is only really stated in and supported by the Declaration of Independence, and not in the documents that actually lay out our rights...at any rate, it doesn't really matter since all of our rights are being slowly taken away anyway
Sometimes, you just need pie...