While I do believe this is a coincidence, (compare how Swedish has broder, syster, fader, moder, but -are as the agent derivation morpheme. (All but syster somewhat restricted to higher stylistic registers or archaic use, having slightly reduced forms in colloquial use - bror, far, mor, with brorsa, syrra, farsa/pappa and morsa/mamma being quite low register).
Now, what if a language has voice- or transitivity-marking agentive (or patientive) affixes, a bit like -ee vs. -er, but including things like reciprocals, and kinship terms were treated as though they were derived from verbs (although they are not). Maybe there could be interesting uses of morphology there, such as -
brother.reciprocal agent.plur = a set of persons who are each other's brothers
my brother.intransitive = my brother (uttered by a woman)
my brother.reciprocal = my brother (uttered by a man)
my fathers.intransitive.vocative = every man that has offspring among my guests!
my fathers.transitive.vocative = my ancestors!
my father.intransitive = my older friend
my father.transitive = my father
Further vague things that might turn into ideas:
- something transitivity-like for nouns, that isn't just possession-related or related to the noun being an agentive form of a verb
- more asymmetric kinship terms (e.g. older brother, younger brother)
- reciprocal passives enabling chains - e.g. fathers.reciprocal.passive = a chain of ancestors (not really reciprocal, but each member of the set but one is the father of a father), parents.reciprocal.passive = one line of ancestors, parents.transitive.passive = all ancestors, ... who knows, there can be any amount of weird semantic things going on here.