As Angry Joe stated, Destiny lacked competent story-telling. Sadly, the intro to the game tells us more about the game than anything else. Players have a right to be upset while having paid for expansions because it does not excuse the missing content and unsatisfying story at release. The intro to Destiny tells us more about the game than anything does. Destiny needs to answer the following questions in the game's story that was missing:
Who are we?
How long have we been dead?
Who are the Awoken?
What are Exos?
Were they built by humans?
How are they related to the humanity's plight?
If the Traveler can bring back things from the dead, how does he even lose fights?
Why can't the Fallen simply attack the Traveler out of low orbit from a distance? The Traveler seems pretty exposed.
The female character in the game who handed us a weapon was very generous but... we don't know her name or anything about her. She didn't want to explain anything even when there was time. The only way to find out is to wait for another expansion in which players will have to pay for.
The Taken King tried to make its story more straightforward and clear, giving many of its A.I. characters more personality and interesting dialogue in the missions. Destiny needs to take it one step further. Instead of including the vast majority of Destiny‘s lore on grimoire cards that need to be read outside of the game, why not turn that information into audio clips that can be played? Or if recording extra audio is too much of hassle, at least make the grimoire entries readable in-game. Basically, players shouldn’t need to seek outside sources in order to understand the lore at the heart of Destiny‘s story.
Include all of this information in the story and try to tell it through gameplay rather than extensive cut-scenes: http://www.gameinformer.com/b/features/archive/2015/08/24/what-s-going-on-in-destiny-s-story-anyway.aspx
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The story is there but most people where too focused on getting to end game quickly so they don't pay attention.