Obviously, GOD allows abortion because it happens; so does HE allow murder, divorce, and all other forms of evil. Why is another subject. Neither can we pick a few verses from the Bible and give those verses the purpose of allowing something we want to do or believe. That is not the purpose of any verse. The Bible's purpose is to give us a picture of a Child of GOD, who is a spiritual being destined to live on a different plane of existence other than the Physical Reality of which we currently consider ourselves a part. GOD even provided us a living example of a Child of GOD (Son) in the form of Jesus.
The primary purpose of abortion is to allow sexual activity outside of marriage without taking the consequences of an unwanted child. This motive is self-serving. Self-serving motives have no eternal value because they are automatically divisive; and what is eternal must be in unity--the same Spirit seeking the same Purpose by everyone according to their gifts and abilities.
On this plane of existence, we need to work to rid ourselves of the self-serving nature while focusing on the highest Purpose of GOD we can envision and contribute accordingly. That nature has no eternal value, and all lifestyles it creates will eventually be destroyed--including those related to abortion, murder, divorce, etc.