Yes, selling bitcoins for fiat feels like betrayal.
Indeed. Sometimes it happens, though. The secret is to not think of it as selling your bitcoins for dollars, but rather as temporarily pawning them to get through an emergency.
It's like a beloved musical instrument. You'd never consider selling it, but you'd let the pawnbroker hold it until you can redeem the ticket. You never lose sight of the fact that you'll get it back some day.