After a brutal (and awesome) fight, Prometheus gave Oliver a terrible choice: he could kill Prometheus, which would save William but activate the dead switch that would set off all the explosives and hypothetically kill all of Oliver’s loved ones other than William.
Oliver had already declared that he wouldn’t give in and kill Prometheus, but it seemed there was no option that didn’t involve Prometheus getting the win somehow.
Alternately, he could let Prometheus kill William to spare his friends.
Prometheus really had the entire scenario on Lian Yu planned out, from recruiting Captain Boomerang to stashing William on an escape boat where he would confront Oliver for the last time.