The word appears in the Torah (ex. Bereishis 10:5, 36:40, Devarim 29:17, etc.) and is in common usage today.
closed as off-topic by rosends, aBochur, Alex, sabbahillel, mbloch Jun 2 '18 at 18:15
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Perhaps ספח, meaning something gathered or attached, as in וְנִסְפְּח֖וּ עַל־בֵּ֥ית יַעֲקֹֽב (Isa. 14:1). Shin is interchangeable with sin and sin with samech, and we already find the root spelled with a sin in וְהִנֵּ֣ה מִשְׂפָּ֔ח (Isa. 5:7). A family consists of biologically gathered or attached individuals.
As he says that the root is the word "shafach", here is the entry for "shafach" p. 844:
He thus claims that the word for "family" comes from the word for "spread out" and, as pointed out in one of the comments, is related to the word for "maidservant.
Rabbi Hirsch in Bereshis 8 19 writes about the word משפחה. He says it has a meaning of
plentitude, of the accumulation, the gathering of many to a mass.
root שפח, related to שפע, שבע, שבע, ספח, ספה, שפה, סבא, צבא etc. All of which have the meaning of plentitude, of the accumulation, the gathering of many to a mass. (By way of parenthesis note how the שפחה, that person who, in the non-Jewish put of view, stands at the very lowest social grade, in the Jewish point of view, as is expressed in the name they give her, is raised to a member of the family).