Tamagotchis are strange creatures. Sometimes they cme from an egg, and sometimes they're born live.
When you first start your tamagotchi, it comes from an egg. Also if you press reset, and select reset on the download or reset screen, it will come from an egg. In both these cases there is no parent information in family listings.
If you mate your tamagotchi using the matchmaker, there will be one live birth baby; no egg.
If you mate your tamagotchi with another tamagotchi by connection, there will be two live birth babies; again no eggs. Shortly after the second baby is born, it will jump off the screen to go live with the father.
Sometimes, if there is a communication error during mating-by-connection, the mother has two babies, the second baby jumps off the screen, but it never appears on the father's screen. In this case the father doesn't recognize that it mated. It is still available to mate with other tamagotchis by connection, or by matchmaker.