This is a pretty common opinion among anti-choice people. One of the many divides in views on abortion is between people who believe life begins at birth vs. before birth, with a significant number of the latter believing life begins at conception.
EDIT: Obviously views on abortion are complicated and vary widely. All I'm saying is that it's really not hard to find people who will tell you life begins at conception (and by that logic, believe that killing a fertilized egg is equivalent to killing a baby).