I believe the phrase suggests that an abortion is the same as a chicken laying an egg. If so, the analogy suggests abortions should not be considered controversial.
As far as using it, you should decide if you agree with the statement once you understand it. One can argue that there are some logical problems with the analogy. If you do use the phrase, you can expect some counter arguments coming your way, such as:
First, an egg that gets cooked in an omelette cannot be compared to a human embryo. An edible chicken egg is just an egg...it did not get fertilized. Abortions do not remove eggs, they remove embryos (an egg that was fertilized with sperm). The proper human analogy to an egg laid by a chicken is the period that a woman has once a month. Also, chickens donīt need operations to lay an egg, but abortions require surgery or advanced medicine.
Maybe Iīm totally wrong about the analogy...but I infer from it an attempt to lessen the seriousness of the abortion debate.