Except that, the mother doesn't provide the egg and sperm cell anything, other than a place to fuse. After the ORGANISM grows and develops to a particular stage, it will attach to the womb and THEN the mother provides nutrients for the growing organism, but the process of life has already begun. You see, in your skin cell example, the process of life was begun by the host of the skin cell, it produced a living skin cell, and other were artificially produced from that one. This could not happen with a dead skin cell, and the skin cell is never able to regenerate itself, or become anything more than a skin cell, incapable of carrying on the process of life.
The sperm and the egg is all that is needed. Both are organic human cells, or human material, but not organisms. They can't carry on the process of life alone, they are like skin cells. Once the conception happens, an instantaneous chemical process begins, it is most importantly noted in the immediate blocking of any further sperm penetrating the egg cell. We now have two fused cells, not one. No other element or material is required from the mother or father, the body doesn't give it something else along the line, it has everything it ever needs to become an organism at this point. It's important to note, the fused cells have not yet met the requirement of an organism, they must successfully generate a cell... but once that happens, the two fused cells, along with the newly-arrived baby cell, comprise a great big happy family known as a living human organism.
Now that's funny!