Missed flight despite being at the gate 2 hours early. Flight delayed numerous times which I understand things happen.Gate changed di t hear announcement. We were sitting very close to the changed gate however. Announcements for multiple flights happening at the same time. We are not old hard of hearing people. Heard our flight being called for group 1 to board. Waited for the remaining groups to be called.We were group 8. We waited for 15 min.thinling there was just another delay. I went to the agent who said the plane had just left.. This was at 3:18. My last email minutes before said it was to depart at 3 30. Our nest were never called when we failed to board and all groups were not called. The employees in this section were so grumpy and appeared unhappy.Blaming us really for our missed flight. This employee who did rebook is saw us there waiting for the 2 hours. The flight staff were great and friendly We ourselves are polite friendly and kind respectful people who are not whiners.I would jave expected the same,service in return at DCA. With all the time in delays and missing the original flight we would have had hours more to tour Washington.