Correct, because personhood is a social construct without any factual basis. Therefore, the personhood argument is insufficient in determining when a human possesses the inalienable rights to life, liberty and the pursuit of happiness.
Tell me, if our DNA does not make us human (which it absolutely does, as DNA controls the structure, development and function of our cells) then what does?
All bacteria possesses DNA. Even some viruses, which are not classified as "life," possess DNA.