No gate available

I'm on a flight right now from ATL to Raleigh that landed around midnight (on time as scheduled). When we landed, the captain announced that there was no gate open and there wouldn't be one for at least 35 minutes so we are stuck here indefinitely. My question is, what are the airport or Delta rules that make this possible? There aren't any flights leaving RDU at this time, so certainly there are gates open in the literal sense, so what stops us from using them?