Old English fæder "father, male ancestor," from Proto-Germanic *fader (cf. Old Saxon fadar, Old Frisian feder, Dutch vader, Old Norse faðir, Old High German fater, German vater), from PIE *pəter (cf. Sanskrit pitar-, Greek pater, Latin pater, Old Persian pita, Old Irish athir "father"), presumably from baby-speak sound like pa.
The classic example of Grimm's Law, where PIE "p-" becomes Germanic "f-." Spelling with -th- (15c.) reflects widespread phonetic shift in Middle English that turned -der to -ther in many words; spelling caught up to pronunciation in 1500s (cf. burden, murder).
