"If two organisms can mate and have viable offspring, and then the offspring can further reproduce, you say the two organisms are part of the SAME species." Fi

"If two organisms can mate and have viable offspring, and then the offspring can further reproduce, you say the two organisms are part of the SAME species." Firstly, that's not true. Even if that were true, there is no evidence of reproductive success between human males and Neanderthal females.