Does this mean you believe the unfertilized egg is not alive?
Does this also mean you believe that the free swimming sperm is not alive?
Would the sterilization of either an unfertile egg or a free swimming sperm be murder?
Correct. They might in some scientific sense be alive, but they do not constitute a human life, even if those little guys are my ambassadors.
Would the sterilization of either an unfertile egg or a free swimming sperm be murder?
No.
The Bible is pretty clear that life begins at conception. The Bible also refers to a "man's hand being stained with semen" as being "indecent" but never says it's immoral or has any semblance of being a life or death matter. The Bible almost certainly would have addressed that differently if it was, given the sanctity with which the Bible treats human life.
What's more it appears that God designed woman for the egg to pass every month wether fertilized or not, and I if I remember biology right, a constant replacement process occurs in the man if the sperm is not used.