We could argue abortion semantics all day long. Heaven only knows that the argument has gone on for centuries. The leap in your reasoning is that if the mother intentionally seeks an abortion, then that amounts to nothing more than murder. However, intentionally ending a life is not always murder. Soldiers on the battlefield aren’t murderers. Nurses who give a dying patient extra morphine to calm the “death throws” aren’t murderers. Terminating a baby that hasn’t yet achieved consciousness and can’t survive outside the womb is quite possibly not murder. We’ll have to agree to disagree on that one.
I don’t think there is anywhere in the US Constitution which gives the federal government the charter to define “when life begins”. For US citizenship, life begins at birth. There are multiple examples of legal precedent which establishes that laws can’t be applied earlier than that. For instance, adoption proceedings can’t begin on an infant until the birth has actually occurred. Yes, there are some laws that have enhanced punishments for the death of a woman while she is pregnant, but that doesn’t necessarily constitute the definition of life or citizenship. The person the law is protecting is the pregnant woman - and her right to chose to continue her pregnancy. In the same manner, the law shouldn’t dictate to doctors which medical procedures they can perform. Perhaps there are other avenues for controlling specific medical procedures but it shouldn’t be federal law; state law maybe; hospital policy - sure, just not federal law.
Keep in mind that the term “abortion” is emotionally charged. However, all early terminations of a pregnancy are considered an “abortion” in medical terminology. If the embryo or fetus is non-viable (already dead), then the woman may have to go through a medical procedure called an abortion to preserve her fertility and prevent sepsis. A woman who is having trouble in her uterus may need to go through a medical procedure called a D&C (the most common form of abortion) to clear out tissue and have it tested - even though she isn’t even pregnant. A pregnant woman may even lose the pregnancy at home, which many people would call a miscarriage, but there is no medical term “miscarriage”; the medical terminology is “abortion”. Yet because of “abortion statistics” which make the untrained mind think that there are thousands of woman getting a medical procedure done as a form of birth control, there are medical schools that are feeling pressured to not even teach these important, life saving procedures. Imagine the number of women who will die, become gravely ill or infertile because they couldn’t have a private conversation with their doctor without government interference.