A fetus is a human organism (this is the consensus among biologists, including pro-choice ones). Induced abortion is killing. You can make arguments as to why this is justified, but that doesn’t change that it is taking a life.
This paper asks the wrong questions. Yes, a fertizilized egg is "alive" in the same way sperm is "alive". The paper essentially uses the question of when the development of a human begins to argue:
1. Anything living is wrong to kill.
2. Human embryos and early fetuses are living
3. Therefore, human embryos shouldn't be "killed"
#1 is clearly wrong, #2 is a misdirect, #3 leads to the author's desired conclusion as a result. That paper based on the presumption that "opponents" argue that fetuses are not biologically living organisms. Fertilized eggs and embryos are living human organisms certainly, but it's not a person yet. Is an egg a chicken? Is a seed a tree? Is a caterpillar a butterfly? Is a collection of human cells with the potential to become a human, human? I believe "no" to all of the above. Potential for development into a more complex living organism is not the same as being that other organism.
https://papers.ssrn.com/sol3/papers.cfm?abstract_id=3211703