Along with always contently competing to be the best, these two could never really get along because of their big egos. Steve truly believed his way of thinking was right, while Tony could only see his side of things.
Team Cap conflict was, in essence, a clash of opposing ethics. Looking to keep the Avengers legitimate, Tony Stark signs the Sokovia Accords, permitting government oversight and control over the Avengers. However, Steve Rogers refused to sign the accords, skeptical of the way it might tie their hands in a crisis.
Their friendship is put to the test and ultimately falls apart during the events of Captain America: Civil War, where they had different views of the Sokovia Accords.
During Tony's first conversation with Captain America since 2015's "Civil War," Tony gets very emotional and gets mad at Steve Rogers. He puts some blame on him for running away and not wanting to register as a superhero with the government to possibly prevent the Thanos snap in "Infinity War" from happening.
Steve Didn't Explain The Starks' Murder To Protect Tony & Bucky. The most likely explanation for Steve Rogers hiding Bucky's involvement in the deaths of Tony Stark's parents would be that he was trying to protect both of his friends.
He likely grew up hearing about how great Steve Rogers was from his father, Howard Stark, which may have created a subconscious dislike him. Then, when they finally met, Tony was less than impressed by this supposed superhero his dad bragged about.
Tony feels resentment over the way his father, Howard, compared him to Steve, and Steve assumes that Tony is selfish and unwilling to make hard sacrifices.
Barnes is notably targeted by T'Challa, the Black Panther, who mistakenly believes Barnes kills his father. Iron Man also strongly retaliates against Barnes after finding out that the Winter Soldier was responsible for the death of Stark's parents while under HYDRA control, and that Rogers hid the information from him.
[1] Despite the many physical dangers that Tony faces as Iron Man, I argue that his greatest foe will always be self-doubts and sense of his own inadequacies. These doubts and supposed failures are amplified by Tony's post-traumatic stress disorder (PTSD).
At the end of Civil War, Cap wrote to Tony and told him he understood why Tony did what he did, and even apologized to Tony for his role in the breakdown of the Avengers and keeping the truth about his parents' death secret.
Captain America is physically stronger than Iron Man, whether with his suit or not. If they both entered a ring-to-box hand-to-hand combat, Captain America would destroy Iron Man in that fight. However, if we consider all features in their respective arsenals, Iron Man would literally toast Cap.
Tony Stark's best friend, James Rhodes, is one of the few to wear the Iron Man armor, other than Tony Stark himself. Although he initially took on the role when Stark was dealing with his demons, Rhodes has reprised the role over the years.
In Captain America: Civil War, disagreement over international oversight of the Avengers fractures the team into two opposing factions—one led by Steve Rogers and the other by Tony Stark (Downey).
The Avengers Civil War was a conflict between members of the Avengers that stemmed from tensions between two factions of the team led by Captain America and Iron Man over their divisive opinions of registering into the Sokovia Accords.
Although he is an extremely skilled marksman, Clint Barton is often considered to be the weakest member of the team seeing as he's just a regular guy with a bow and arrow.
It turns out anyone able of holding his hand out can, doesn't it? Only people who are considered worthy are able to wield mjolnir. Cap was deemed worthy in endgame, that is why he was able to hold mjolnir.
Steve Rogers is one of the few mortals able to not only lift Mjolnir, but wield its full power, making him someone who legitimately could defeat Thor. Assuming the reason for their battle is due to Thor being deceived, possessed, or otherwise out of his mind, Cap would be able to use Mjolnir against him.
However, while Tony did make amends with Steve, he wasn't able to do so with Bucky. In fact, they didn't even get to have any interaction before Iron Man's death.
James Buchanan “Bucky” Barnes enlists to fight in World War II, but eventually literally falls in battle. Unfortunately, the evil Arnim Zola recovers him and erases his memory, turning him into a highly-trained assassin called the Winter Soldier.
Bucky had resentment towards Sam for giving up the shield. The therapy session showed the issues they had towards each other. Bucky wanted to know why Sam gave up the shield that Steve trusted him with and was Steve's whole legacy. Bucky emotionally says that if Steve was wrong about Sam then he was wrong about him.
Steve truly believed his way of thinking was right, while Tony could only see his side of things. They never backed down from their own beliefs, thinking their way was the only way, which caused a lot of tension, not only between them but The Avengers as a whole.
He wanted to stay grounded as a friendly neighborhood Spider-Man before moving to the big leagues, and his decision will have a lasting impact on the future Young Avengers. If Peter had accepted Tony's original offer, it would've rendered the Young Avengers almost pointless.
To Iron Man, Captain America committed the ultimate betrayal of his own morals, and to do this directly at him -- someone Rogers spent an entire movie calling out for the same motivation --would be the ultimate breaking point.
