The three branches of pro-choice arguments: undervalue, dehumanize, and manipulate
I will try to summarize the arguments I hear from the pro-choice side. Note that this is about abortion-at-will, not about abortion to save a life (when the mother is in an unhealthy pregnancy).
Undervalue
This is simply believing that human lives a mere biological instance and don't have intrinsic value. While it is a rare argument that is openly put forward by pro-choice, in my opinion it is the most consistent and powerful argument they have. And it lies underneath most of their common arguments.

The reason they don't make that argument is that they know it would invalidate all arguments about human rights (including the rights they claim to defend).

When it is put forward though, you would have to go beyond politics and enter the religious/moral world to discuss this. But ultimately, you cannot convince someone to value anything, and if they decide to reject the value of human lives, discussions are likely a lost cause. Only pray, preach, and vote. Always be peaceful.

Dehumanize
Many pro-choicers claim fetuses are either not humans at all, or not humans enough. It is an unfortunate feature of humanity - believing those who do not look like us are not as human as we are.

It can come in the form of acknowledging fetuses as humans but with no rights to exist in the womb, or simply denying that fetuses are humans. Obviously fetuses are biologically humans, so it should be easy to refute arguments that deny that - just point to a biology book. Here are some of the arguments I see often:

*"Fetuses aren't humans. They are just clumps of cells" - Not much to say about this one. If two humans reproduce, their offspring is by definition a human. And all humans are clumps of cells.

*"Fetuses are humans but parasites" - While not many pro-choicers like saying this, it is how the pro-choice ideology treats fetuses. This indicates that because a fetus is living inside its mother

*"Life starts at birth" - Birth doesn't add anything to the fetus' life... it just makes it independent. This goes back to believing only independent humans can be valued and considering other humans as parasites.

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