I appreciate that you are using logic to inform your beliefs and not just emotion, as most do. Here is my take:
If it is growing, it is alive.
Human life is more precious than other life form. We are the pinnacle of God's creation, the only creature to whom God gave an eternal soul. We are "knit together in our mothers' wombs" and are "fearfully and wonderfully made" (Psalm 139).
If the "clump of cells" has unique DNA, it is therefore a unique human life.
A miscarriage isn't the result of God deciding to kill the fetus. Miscarriages occur for the same reason any person's life ends.
None of us will survive without life support. An unborn baby just needs a different form of life support than what humans require after birth. Once born, we need certain environmental conditions to survive. An unborn baby's life is sustained by his/her mother via the placenta.
Why is a human fetus not given the same protection as an eagle's egg? If an embryo isn't life, why should an eagle egg be protected? Why should an eagle egg get more protection than a human embryo or fetus. I would guess that some would argue that the eagle egg is potential life, not life itself. If that is the case, why should we not encourage the development of a child's life potential knowing that people are the pinnacle of God's creation?
To Joe's Place: We give birth certificates to babies who have been born. They aren't life certificates. That baby didn't suddenly become alive when it exited the birth canal.