What is the story the quests are trying to tell?

[Rex]

I guess the story is much deeper for those of us that were in 1.0 since we basically played the prologue of 2.0 in a sense.

Normally I wouldn't even give you a straight answer since it sounds like you don't even try to pay attention to the dialogue or cutscenes...so let me break this down for you because I'm sure you'll say "TL;DR" if this gets too long too.

1. Garleans are trying to take over the world.

2. In the beginning of 1.0 Beastkin were not a threat, in fact there were some times where you had to play a mini game with them.

3. Garleans started posing more of a threat in 1.0, Beast tribes started to fight back by gathering crystals to summon their Primals.

4. Beast tribes now our enemies because Primals are a threat to Eorzeans and the very "life force" of the planet, the "Aether," takes a huge toll whenever a Primal is materialized. Because of these reasons, we have to defeat Primals. Beast tribes now our enemies because we are killing off their deities.

5. Garleans provoke Beast tribes to summon their Primals so that they can use their powers against them and the rest of Eorzea.

6. We stop Garleans from advancing by killing off their leaders and keeping Primals at bay at the same time.

That's basically it.

Also, just like each tribe has their deity, We have our Goddess. Hydaelyn. The crystal you speak to is Hydaelyn. We don't know if she'll take on any kind of form other than that yet.

That's why we're chosen to fight the Primals because they can't effect us by making us their followers since we're already "touched" by Hydaelyn.

The Echo power is also granted to us by Hydaelyn. Like in the last battle with the white light that's basically just an affect for the last battle to make it seem like you're all powerful.