Thanks for being specific. This is the central issue of the abortion debate. No sensible person would argue against the right of a woman to remove a lifeless lump of cells from her body (eg having a cyst or tumor removed), but most people don't think it moral to kill a fetus in the womb one day before birth. So at what point along the continuum from conception to birth does the fetus become an individual person with natural rights? Of course we can randomly pick a date to grant an individual rights (such as after the first or second trimester), but shouldn't a life or death decision be based on some firmer footing than an arbitrary guess? Perhaps when deciding to strip an individual of life it is better to err on the side of caution. Conception is a distinct, scientifically verifiable event that we know leads to the creation of a new individual. Lacking any other logical date for granting rights to a new life, conception seems a sensible choice.
How about at the detection of an individual heartbeat. Conception is the division of two specialized cells. Not specific enough. More specific would detection of a separate entity. A heartbeat. By this standard, at week 8, there is someone alive in a woman's body that is going to grow beyond the parameters of that woman's body given the right environment and time.
Conception is the fusion of two specialized cells, and the combination of genetic material initiates a biological pathway that results in the birth of a new individual. Regardless, yours sounds like an arguable position. Certainly better than selecting a date arbitrarily.