Abortion is unlike any other issue debated today. Millions of American women have aborted a child, and the pain, loss, and emotional need to justify what was done, both on the part of the mother and on the part of her loved ones, is strong and deep. This means that, in any debate, you may face an invisible thumb on the scale so that even the best logic will fail to persuade. The best you can do is arm yourself with the facts and deliver them in what you hope will be a winning way for your audience -- meaning you will need to make your case, in most instances, not in the language of faith or religion but in the language of the post-modern secularist.
Arguing from Science
The "classic" arguments from the other side collapse under the weight of science. Establishing the evidence of the beginnings of human life will ground your argumentation in science, giving you a much firmer foundation for additional arguments and preempting the charge that you are basing your position on faith or religious belief.
The scientific facts:
1. At the moment when a human sperm penetrates a human ovum, or egg, generally in the upper portion of the Fallopian Tube, a new entity comes into existence. "Zygote" is the name of the first cell formed at conception, the earliest developmental stage of the human embryo, followed by the "Morula" and "Blastocyst".
Is it human? Is it alive? Is it just a cell or is it an actual organism, a "being?" These are logical questions. You should raise them, and then provide the answers. The zygote is composed of human DNA and other human molecules, so its nature is undeniably human and not some other species. The new human zygote has a genetic composition that is absolutely unique to itself, different from any other human that has ever existed, including that of its mother (thus disproving the claim that what is involved in abortion is merely "a woman and her body").
2. It is also quite clear that the earliest human embryo is biologically alive. It fulfills the four criteria needed to establish biological life: metabolism, growth, reaction to stimuli, and reproduction. Finally, is the human zygote merely a new kind of cell or is it a human organism; that is, a human being? Scientists define an organism as a complex structure of interdependent elements constituted to carry on the activities of life by separately-functioning but mutually dependent organs. The human zygote meets this definition with ease. Once formed, it initiates a complex sequence of events to ready it for continued development and growth.
The scientific evidence is quite plain: at the moment of fusion of human sperm and egg, a new entity comes into existence which is distinctly human, alive, and an individual organism - a living and fully human being.
There are many other fact-based arguments that can be persuasive, including legal arguments that prove the Supreme Court in Roe v. Wade did not create a limited right to abortion but a virtually unlimited right to abortion throughout pregnancy.
When you argue with liberals using faith-based or religious beliefs, their eyes will simply glaze over. To be effective, you must argue in the language of the post-modern secularist. That means science and the law.