Why when we pray for someone’s health we mention their mother’s name, and when we call someone up to the Torah we mention their father’s name?
Generally a person is called by the name of his father, which in essence is his family or last name, because lineage goes through the father. If the father is from a certain tribe or the father is a Cohain (of the priestly tribe) then that factor is passed on to his children.
The reason that we deviate from this when praying for a sick person is explained in a couple of different ways: first, concerning King David it says “save the son of Your maidservant“ (Psalms 86:16). Since it mentions David in the course of prayer being mentioned by the name of his mother and not the father – we do the same in our prayers.
Others explain that the only parent one can be sure of is the mother and when asking for mercy we should make sure that our prayers are exact. If we mention the name of the mother we can be sure that the name is correct.
Another approach is mentioned in the Talmud Shabbos (66b) — Abaye said, “Mother told me — all incantations are recited with name of the sufferer’s mother.â€? Some explain that, in general, women have more spiritual merits than men. This is due, in part, to their exemption from many commandments including the study of Torah. As a result, men have more “negative angelsâ€? against them (bringing them up on charges of forsaking the commandments) than women which might prevent the prayers from being accepted.