Just wondered why I, as Dragon Born, wanting to salvage the world from its end, meet so much resistance concerning this exact notion?

Or let me ask you this way; Why wouldn't you want to save life on earth?

Parth won't and neither will the Greybeards. They seem likely wanting the destiny of the world to run its own course. Which I kinda understands, but yet, at the end, they help me.

It may just be me over thinking, but I'm kinda all over the place lore-wise.

If I could decide, solely, I wouldn't take orders from anyone, well not ANYone, but definitely not those who take advantage of my gift. I would like to see Delphine and Esbern's heads at the end of my Volendrung. And I feel gutted having to work for them, being treated as trash - or as a tool, even.
Yet I do wan't to complete the main quest, but I don't know why...

I wouldn't blame anyone for now responding to this bewildered nothing, though it would be nice if you did so.

Trust me alot of ppl feel the same way about Delphine and Esbern. I felt like their should have been more dialogue choices with them, mostly telling them to shove-it where the sun don't shine. ( or words to that effect). I don't like being told "do this or else", in real life, so in a game, I'm probably alway's going to do the opposite if given the oportunity.

Paarth and the Greybeards basically left me with the feeling that they, while willing to help the Dragonborn, would let the world end without lifting a hand themselves to stop it. But the way they look at it, it may not be an end, but more like an end to this "world" and a start of the next "world".

I agree, really.
And yes, reg. the Greybeards, I got that feeling as well. That they would pretty much stand still doing nothing as the world was about to end.