Why sixteen? Lists differ
The number of saṃskāras is not fixed in the texts. The Gṛhya Sūtras each give their own set, and the Gautama Dharmasūtra counts as many as forty. Over time the list of sixteen became the most widely quoted, especially through later manuals.
Even within the sixteen, names and order vary slightly — for example, some lists include Vedavrata rites or separate the ear-piercing. Don't worry if your family's list looks a little different; that is normal.