1. You might be attempting to join a quest that has a pre-requisite
Some quests may have pre-requisite quests. In such cases, you need to have at least joined the pre-requisite quest, before you can join the next quest.
2. You might be attempting to join a repeated quest
If you already participated in a repeated quest and got rewarded, you will be unable to join this new repeated quest, to give other players a fair chance.
Check out this article on What are pre-requisite and repeated Quests?
3. The quest has not started yet
Quests are only available for registration on the start date and time indicated.