I'm not sure what information you have been given but you do not have to complete the Binding Coil of Bahamut to progress in the main storyline - the Coil storyline is actually an optional story that ties into the main storyline but isn't a requirement to progress in it (although there is a scene in the Heavensward 3.4 story that does reference it if you have passed it already, but again it's not a requirement to progress through this quest, it has alternative dialogue if you have not done Coil).

If you are unsure whereabouts you are up to in the main scenario open your Journal and check under 'Seventh Astral Era Main Scenario Quests', take note of the last quest title in this list, and then post it here, so I can help you with where you need to go, as it is not always obvious where you last left off on the main storyline. Either way, don't give up yet!