No, humans would not become extinct if everyone identified as homosexual. Sexual orientation does not directly impact the ability to reproduce or the survival of the human species. While same-sex sexual relationships do not result in natural reproduction, humans have various methods available to reproduce, including assisted reproductive technologies such as in vitro fertilization, surrogacy, and adoption. Additionally, sexual orientation is not determined solely by genetics, and even if there were a hypothetical scenario where everyone identified as homosexual, it would not prevent reproduction through these alternative means.
It's important to note that sexual orientation is a complex and diverse aspect of human identity, and it has existed throughout history in various societies and cultures. The continued existence and survival of the human species depend on a range of factors, such as maintaining a sustainable population, ensuring access to resources, and addressing other social, environmental, and technological challenges. Sexual orientation, whether it is predominantly heterosexual, homosexual, or any other variation, is not a determining factor for the future existence of humanity.