Tony Stark is, and by all accounts will continue to be, the lynchpin of the Marvel movie franchise; he was our way into that world and continues to be the central figure that looms large even when he's not physically present. It speaks volumes that Iron Man is the primary protagonist in both Avengers movies, despite a wide array of complex characters to choose from.
However, The Avengers: Age of Ultron had no shortage of emotional turmoil for all of our heroes. Iron Man created an artificial intelligence that wound up being Machine Hitler. The Hulk and Black Widow were torn apart just as their romance was blossoming. Hawkeye had to say goodbye to his family. Scarlet Witch and Quicksilver were manipulated by Ultron, not to mention the latter killed in a hail of gunfire. Thor realized that Captain America might be able to pick up his hammer.
But there's one heartbreaking development in the film that often seems to go unmentioned, which is the breakup of the best couple in the entirety of the Marvel Cinematic Universe: Tony Stark and Bruce Banner, a.k.a The Science Bros.
In The Avengers, Tony and Bruce coming together is a beautiful thing to witness. Two loners, so often left to their own devices when it comes to discussing their science mumbo jumbo — Tony alone in his workshop, Bruce hiding in third world countries trying to cure himself — are united in pure scientific bliss. They trade ideas and theories, working as a think tank to find a solution to the greatest threat the universe has ever seen. It's a match made in science heaven as the solitary twosome find solace, comfort and respect in one another.
This is further explored, albeit briefly, in the tag scene of Iron Man 3. Shane Black's film is the story of Tony Stark dealing with his inadequacies as a hero, the fallout from the Battle of New York, and creating a legion of A.I.-driven Iron Man suits (that would later come back to haunt him) in an effort to be everywhere at once. This is not a story a prideful man like Tony would share with just anyone, and as we see in this scene, he's not. He's sharing it with someone very specific.
The post-credits scene reveals that the voice-over narration of the film was spoken in confidence to a Bruce Banner struggling to stay awake. It's a humorous scene that depicts the two characters like old friends. With that friendship comes implicit trust, defining Bruce as someone Tony feels comfortable sharing his most personal stories and thoughts with, let alone riffing on science. In fact, Bruce Banner is the only character other than Pepper Potts that we ever see Tony be emotionally intimate with in any fashion, platonic or otherwise.
This is why Bruce's decision to exile Hulk in Age of Ultron is so devastating. It removes a key externalization of Iron Man's development from self-centered billionaire (playboy, philanthropist) to the hero we saw willingly sacrifice himself to save New York City from the alien incursion.
Taking this away from him would most likely cause Iron Man to retreat inward, reassessing his current circumstances with no room to really vent about them to a peer. It wouldn't be all that surprising to see these emotions play a central role in his position in Captain America: Civil War; he's blaming himself for the events of Age of Ultron and as a result ramps up a conflict born of his own shortcomings as a leader that begins to erode the team.
With a conflict looming and Tony desperate to find new allies, signs point to the incorporation of Spider-Man as more than just exciting fan service and an excuse to beef up the cast of characters/slate of movies. Given how true to its characters and source material Marvel Studios has been over the last eight years, it's likely that its take on Spidey will be every bit the science genius that his comic book counterpart is.
Tony probably sees much of himself in Peter Parker, a young genius doing what he can for the greater good. Likewise, it's probable that Peter sees Tony Stark as an aspirational figure; it wouldn't be shocking to learn that the emergence of Iron Man and the Avengers played a part — along with the death of Uncle Ben, of course — in Peter deciding to use his powers to become the Web Slinger.
Tony could recognize the opportunity to groom him to become his new Science Bro, so to speak, in the form of a mentor/mentee relationship. It's an interesting potential development, considering this also means that Iron Man is effectively drafting a minor into the fight (technically not the first time, either, if you count Iron Man 3's Harley Keener), suggesting that maybe his desperation has blinded him to the consequences of his actions.
Subsequently, this could put Peter in the position of having to choose between remaining loyal to his idol and a philosophy he doesn't necessarily agree with; a conflict that could be carried over to Spider-Man: Homecoming — which Iron Man is scheduled to appear in.
The possibility of having Spider-Man be more than just a new member of the team (or the Marvel Cinematic Universe at large), but rather a personification of Tony Stark's desire to make different choices, or at least rectify the poor ones he's made, would work within the larger tapestry that Marvel Studios has constructed with Tony at the center.
And if we're lucky, we'll get to see Tony and Peter geek out over Spidey's web shooters, and we'll be better for it.