patronymic (n.)

Middle English fader, from Old English fæder "he who begets a child, nearest male ancestor;" also "any lineal male ancestor; the Supreme Being," and by late Old English, "one who exercises parental care over another," from Proto-Germanic *fader (source also of Old Saxon fadar, Old Frisian feder, Dutch vader, Old Norse faðir, Old High German fatar, German vater; in Gothic usually expressed by atta).

This is from the PIE root *pəter- "father" (source also of Sanskrit pitar-, Greek pater, Latin pater, Old Persian pita, Old Irish athir "father"), which is presumably from baby-speak sound "pa." The ending formerly was regarded as an agent-noun affix. The classic example of Grimm's Law, where PIE "p-" becomes Germanic "f-."

The spelling with -th- (15c.) reflects a widespread phonetic shift in Middle English that turned -der to -ther in many words, perhaps reinforced in this case by Old Norse forms; the spelling caught up to pronunciation in 1500s (compare mother (n.), weather (n.), hither, gather).

As a title of various Church dignitaries from c. 1300; the meaning "creator, inventor, author" is from mid-14c.; that of "anything that gives rise to something else" is from late 14c. As a respectful title for an older man, recorded from 1550s. Father-figure is from 1954. Fathers "leading men, elders" is from 1580s.

My heart leaps up when I behold

  A rainbow in the sky:

So was it when my life began;

So is it now I am a man;

So be it when I shall grow old,

  Or let me die!

The Child is father of the Man;

I could wish my days to be

Bound each to each by natural piety.

[Wordsworth, 1802]

"a name derived from a mother or maternal ancestor," 1794, a hybrid from Latin māter "mother" (see mother (n.1)) + Greek-based ending from patronymic. As an adjective, "pertaining to or being derived from a mother or maternal ancestor," from 1874.