From the instant of conception, there is a living cell by every definition of life in every biology textbook.  At that same moment, this life has unique, human DNA.  Therefore it is human.  Therefore a human life begins at conception.  Scientifically, it really is that simple.

The only other argument that I have heard that has even a hint of logic is human life beginning when there is a heartbeat, since someone is normally declared dead when their heart stops.  I'd argue that is a false equivalent, though.  My old parts manager was working in his yard and had a heart attack.  His heart stopped beating.  Luckily a neighbor saw him drop to the ground, called 911, and an ambulance happened to be a block away and got there and restarted his heart.  He lived many more years, but moved away a bunch of years ago, so I have no idea if he is still alive.

If he had dropped "dead" when his heart stopped and I had walked up and shot him in the head permanently "killing" him before the ambulance got there to revive him, would I be guilty of murder?  Yes, I would.  In the same way, anyone killing a person from the moment of conception to natural death is guilty of murder.

FYI, most contraceptives, like the pill, prevent implantation and therefore kill the baby just like a mother withholding milk from a newborn.