You are wrong. To me, a born infant is a person. If somebody says, "I wouldn't mind if it were legal to kill a born infant," I would merely find that distasteful. But if somebody says, "It should be legal to kill a born infant," I will say a great big "No" and stand, speak, and vote against that with the power of my own life and liberty.
For me, when it's inside the woman's body and receiving life from her life, it is not a person, but when it's outside her body, it is a person. I make a complete distinction between these categories, supporting the woman's right to choose when it's inside her body, while accepting that states have a right to ban abortion after viability if they make exceptions in case of threat to the woman's life or health as medically determined, and supporting the born infant's right to life. I agree with Roe v Wade and Planned Parenthood v Casey. So do many millions of other pro-choice people.