Nope, that's not what we need. Classical liberalism doesn't establish that fetuses in the first trimester are persons with rights and responsibilities. For instance, Kant said a person needs the power of reason to legislate his or her own behaviour, and Locke said personal identity is due to connections between memories. A fetus has neither.
Sure, adults should take responsibility. But that point could just as well count against birth control. Again, there's what the conservative says he believes, and there's what he actually wants. He co-opts liberal principles and uses them as pretexts for the old-world patriarchy he craves. The real responsibility of mothers, according to conservatives is to obey the sexist presumption that women should be confined to the home to care for the many children that would ensue, given the lack of such crutches as birth control and abortion.
Classical liberalism proved to be flawed, which is why it was updated with more progressive principles--because unlike conservatives, liberals and humanists learn from their mistakes. It's no surprise that liberalism was flawed since racist imperialism, patriarchy, and slavery were still in place in early-modern Europe and America. Early liberals were laissez-faire about the economy, and history showed that that deference to capitalism led to plutocratic control over democracies.
I don't overlook anything. I deal with libertarianism and the conservative appeal to classical liberalism elsewhere: