erübrigen

From er- +‎ übrig (“remaining, left over”) +‎ -en, hence “to leave over, have as surplus”. Accordingly, the reflexive sich erübrigen actually means “to be left, remain” and one would originally say es erübrigt sich, etwas zu tun in the sense of “XY still remains to be done”. The quite opposite contemporary sense seems to emerge around 1900. It probably developed through confusion with the active verb in the sense of “to spare”. Moreover, that which is left to be done last is often the least important thing and may in fact become redundant through developments in the meantime.

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erübrigen (weak, third-person singular present erübrigt, past tense erübrigte, past participle erübrigt, auxiliary haben)

1. (transitive, dated except with können) to leave over, have extra, put aside, spare

   Er hatte etwas Geld erübrigt. ― He had put aside some money.

   Sie gab alles, was sie erübrigen konnte. ― She gave all she could spare.

2. (reflexive, of actions) to be or become gratuitous, redundant, no longer necessary

   Nach allem, was wir heute wissen, erübrigt sich diese Frage.

   With all we know today this question has become redundant.

3. (archaic to obsolete, reflexive, also intransitive) to be left, to remain to be done

   Abschließend erübrigt sich noch, historische Beispiele für beide Fälle zu geben.

   In closing, it remains for us to give historic examples for both cases.

• “erübrigen” in Duden online
• “erübrigen” in Digitales Wörterbuch der deutschen Sprache