The strongest arguments against abortion don't hinge on whether the fetus is a person. The question of abortion ultimately boils down to whose rights we privilege: those of the mother, or the fetus?
"Potentiality" - this view argues that regardless of whether the fetus is a person, it has the potential to become a person, and thus inherits some moral consideration.
"Value of Human Life" - the argument that human life - at any stage of development - has intrinsic value and thus should be protected.