Gorgon has a huge point here. You are simply writing off the sperm and egg when both are need to create zygote. Furthermore, only certain sperm have the correct proteins needed to fertilize an egg as well as only some eggs are viable for fertilization. By your logic we should find these certain eggs and sperm inside each human and make sure they are not wasted because it is these components that add up to a potential human life.
My point was that the individuality of a person is determined by DNA. That DNA is first seen in the zygote formed by the egg and the sperm. That is why I believe a fetus is a person, but an egg or a sperm, individually, is not.
That would only be a logical argument if a person was the equivalent of his or her DNA. This is untrue. The DNA is a building block for the person, as proven by identical twins.
The nature Vs nurture debate has boiled down to behaviorists, who say that you are born with a tabula rasa (blank slate) and everything about your personality is learned. This is a ridiculous statement, because studies have proven that some people have, for example, higher natural aggression. Then there are those who say we are predetermined to be who we are, which is also proven wrong (most identical twin studies show nurture is more important than nature). It comes down to most modern and reasonable scientists agree that it is a match somewhere in the middle, the question is is it 50/50, or mostly nurture? I don't think I've run into many recent studies that try to say that who we are is mostly nature.
Imagine a person to be a nice radio, with bass, treble, left and right, volume and forward and backward tuners, an FM/AM switch and seeking track, favorites--all of the bells and whistles. The DNA would be what everything is set at when you get the radio. Then, over your life, you may change the presets according to your nurturing/the situations that you find yourself in. Things like how you are raised, personal experiences, who you are friends with, etc. will slightly alter your radio to make it what we would really consider the person.
Nobody looks at a person and says, "He has blond hair and blue eyes, that is who he is." What makes a human distinct isn't the DNA itself, but how the DNA is used to make a person. The individuality of a person has very little to do with the DNA, as I'm sure you've met two people who are almost exactly alike, even if they look different.
And, according to your argument that origin of individuality is the point that we should consider it a person, it shouldn't be considered a person until it's experienced, which means probably not until birth or after. That is, of course, ridiculous, because you could easily argue that a baby hasn't consciously experienced and started to gain individuality until the second, sometimes the third month, when it actively shows emotion and has a mostly fully developed brain.