When does a person begin?

A well derived argument found in the Articles section for the Andrew Tallman Show:

Working solely with the calendar of Elizabeth’s pregnancy, Luke has told us that Jesus was a person with sufficient individual identity that His cousin could recognize him through the assistance of the Holy Spirit.(1:41-44) But Luke has also told us that when this occurred, Jesus could only have been a maximum of four weeks old and probably was much younger than that.

Gabriel announced the conception to Mary in Elizabeth’s sixth month.(1:26) Thereafter, Mary traveled to the hill country (1:39), where she stayed for about three months (1:56) before leaving prior to John the Baptist’s birth (1:57). This means that fetus Jesus must have been less than four weeks old when she arrived, a maximum given the parameters. But, given the fact that she went immediately and in haste (1:39), a much more likely reality is that He was only a few days old (perhaps not even implanted yet) when John recognizes Him. Mary certainly wouldn’t have even been able to know by ordinary means that she was pregnant yet.

So the pressing point of all this analysis is not that John in his third trimester was a person in the womb when he leapt for joy. The unavoidable and much more forceful point is that Jesus was in the very earliest portion of His first trimester when He was recognized by John as a person. And unless Jesus is not a human child, this means that all children are people at this early stage.