Sperm are not children. A Fetus is a child. Drawing such a comparison to half of the undeveloped genetic material is emotional, if not retarded, rubbish.
You used the term "live on its own". Should that be the guideline for murder? No human child can live on their own for several years after birth. So tell me, what makes birth so special as to be your ultimate delineation? Premature babies can survive up to 4 months early. A two year old is cheaper but no more independent, especially if they have medical needs.
There is no fine line, no clean delineation. Not if we are to compromise between NEVER and ALWAYS. This has to result in a grey area and for legal reasons we must choose what that is. We are taking a hot topic, with something undefined, and giving it a definition to suit our purposes for a compromise. Setting it at birth would not be a compromise. Neither would conception. So I offer a clear path forward, ALL the abortions you want - so long as they are done quickly and early in the pregnancy. First trimester being ideal, second being opposed, third being off limits. More reasonable people than us would need to negotiate over the second trimester.
That is a healthy and constructive approach to abortion. Which I am sure fanatics on both sides would oppose. Where would you truly stand, I wonder?