Society exists to equally value the protection of all it's members if it is a free state.
The protection of the weakest and least able to protect themselves must be the most important act of protection the state can accomplish.
If the state does not protect it's most vulnerable first, it is not a state for everyone, it is a slave state.
Fetuses are the weakest and least able to protect themselves in society if they are persons for the purpose of society.
Personhood ends when the brain stops working so it must begin when the brain starts working.
The brain starts working at the end of the first trimester.
If personhood is directly related to the working brain, abortion after the first trimester is a balance of multiple person's rights.
If protecting the most innocent is a value of society, we must take the most possible care when dealing with the most important right of our most innocent people and err on the side of caution.
There are numerous ways to rearrange these priorities, for example to say that personhood does not being until a being is self-sufficient or that whoever has been around longest should decide, etc. This is a contingent calculus. IF you value protecting the innocent AND you accept the working brain as a primary criteria for personhood THEN there are really only two ways to potentially justify abortion - rape and quality of life due to genetic disease. But that's a different subject. I don't believe there is any way to ethically rearrange these priorities so that abortion is acceptable in any but those particular exceptions.
Rape - to insist the mother endure a pregnancy not of her own choosing would be insisting on torture and no person or government has the right to make that decision for someone else. <genetic disease is obvious>