MCU Film Theory: Nick Fury Has Been An Alien ALL ALONG
It would make sense that Fury would liaise with the Skrull at this point, seeking their help in developing defences and unlocking the keys to the Tesseract. Unfortunately, he also made the mistake of handing it over to Selvig while he was possessed by Loki and drawing the God Of Mischief's attention to Earth in the process. Any plan he then had to take the Tesseract off-planet to help develop defenses or even to explore it were derailed badly.
This would all suggest that the Fury in The Avengers is a Skrull stand-in, which might be a hard prospect to accept, but his behaviour doesn't entirely contradict it either. After all, would the real Fury have failed to detect the Avengers uncovering SHIELD's Phase 2 plans on the Helicarrier? Would he really have trusted a known problem child of the programme - Tony Stark - with access when he knew what he was capable of?
And even more crucially, would the real Fury really have used the death of his friend in such a cynical way to bring the Avengers together? That trading card ploy feels a lot more like the trick of someone fundamentally more well-versed in duplicitousness and deception. In other words, it's a Skrull.
The next time we see him in the movies - after he helps revive Coulson with Kree blood, which you definitely have to assume would be Skrull knowledge in Agents Of SHIELD - is in Captain America: The Winter Soldier in which he apparently fakes his own death and then goes underground after SHIELD's infiltration by HYDRA is revealed. Even that very infiltration and Fury's lack of awareness of it suggests he wasn't quite on his game. Or he wasn't himself, in other words.
Not only is this not Fury, but it's two different Skrulls posing as him while the real Fury is off-planet. The first is legitimately killed by The Winter Soldier - a pawn sacrifice designed to give the real Fury a break from duties on Earth so he no longer has to keep his Skrull facade up. That's how his death is so convincing. When he reappears at the end, it's simply another Skrull who tells Cap that Fury is heading off to take down some remaining HYDRA bases in Europe.
We see him do just that - at least partly - in Agents Of SHIELD, after which he tells Coulson that he's going off-grid for a while and that the new Director of SHIELD shouldn't worry about him being "nowhere" since he will be "everywhere." If that's not a tongue-in-cheek confirmation that Fury has the ability to be wherever he wants thanks to his Skrull accomplices, then it's a hell of a coincidence.
Even Fury's gravestone in The Winter Soldier seems to hold a hint at the truth of his fate and where he actually is. While the inscription may have looked like nothing more than an Easter Egg reference to Samuel L Jackson's work on Pulp Fiction, the verse actually hints that Fury is off with the Skrull helping them:
“Blessed is he who, in the name of charity and good will shepherds the weak through the valley of darkness for he is truly his brother’s keeper and the finder of lost children ”
A "finder of lost children"? Shepherding "the weak through the valley of darkness"? That might as well be them spelling out that Fury is off helping the Skrull find their missing refugees as well as working with them to try and develop better front-line defences for Earth. They are, after all, the most gifted scientific race in the known galaxy at this point, and it's not like the idea of Fury and the Skrull's developing something in space is plucked completely out of thin air - it's literally what we see them doing in the Far From Home post-credits.
And not only that, the scene shows the Skrull armada of ships has been rebuilt, which wouldn't be a quick or simple thing to do. It would make sense that that would be a first phase in using the Skrulls to become an effective aid in Earth's defence. And then focusing on building the space station - the MCU's version of SWORD from the comics - as a means to defend Earth against other threats like Thor, The Destroyer, Loki, the Chitauri and God knows what else would make sense.