If you fly first class you can "offer" to give up your seat if the flight is overbooked just as you do in coach. The airline does not take coach volunteers first. When a flight is overbooked it means that there are too many people (or too much weight) for the whole plane. It doesn't matter which class of service you are booked in. However; if first class is not available on the flight they reschedule you for, you will end up in coach and a pleasantly surprised person who was on your original flight will be enjoying your first class seat!