Let's backtrack a bit, to the time when Peter was following Steve to take down the Hydra base,
After Shiller took over Hydra's duties, the Avenger Squad's operations started to go awry, which upset Peter a bit, so he called Shiller for some comfort.
He understood the reasoning that Steve explained to him, but it was always tough to recognize some of the feelings of loss. Previously, Peter had stayed in Shiller's therapy clinic for a while, during which he could directly consult Shiller with any emotional problem he experienced.
He thought it was the most emotionally stable period in his life, it felt great, so even after leaving, he missed that time.
"My Uncle Ben often said that in the world of adults, failure is routine. You might have to experience many failures before you achieve a single success."
"I understand what the Captain means too. Even in study and exams, it requires a term's time, let alone dealing with such formidable spy organization as Hydra."
"However, previously, our operations were quite successful. We captured many Hydra agents and avenged the poor victims."
"At that time, I was overjoyed, but recently, I've seen more sickeningly horrendous experiments in Hydra's base, yet we cannot catch the mastermind immediately... "
"Every time I think of what the victims have gone through, I find it hard to breathe, and it's even more unbearable thinking that those evil people might threaten others."
Peter sighed on the phone, and on the other end, Shiller asked him, "Where are you now? Inside the Avengers' base?"
"Yes, they're discussing tactics outside, and I'm making this call from the lounge. I'm a bit worried that they'll hear and think that I..."
"Your base should be underground, right? You should change location, go up to the surface and find a café with French windows to sit for a bit."
"Adults can most times handle pressure from various aspects, including work problems, relationship issues, living conditions without sunlight, etc., but that doesn't mean that minors can as well."
"Especially when you're dealing with adults, who are not ordinary people, their psychological resilience is much stronger than yours, so you may find them nonchalant, but that only adds to your stress."
"Perhaps, in this kind of comparison, you may feel weak, and belittle the difficulty of the task, thinking that it's because of your lack of ability, but in reality, it's not."
"So do I have to go out now? Anyway, I need to go home and get some clothes."
As Peter talked, he walked out with the phone in his hand. Steve and Stark saw him, both of them greeted him, and Peter responded with a smile. But once he left the crowd, his expression turned downcast.
He said, "You're right, Doctor Shiller. As you said, I feel like they don't care about these failures at all, making me always wonder, am I overthinking?"
"It's okay. Even though therapy may slightly alleviate your emotional stress, it's not a fundamental solution, I believe we can try some fundamental methods."
"Fundamental methods? What do you mean?"
"I mean, take down Hydra."
Peter let out an exasperated, bitter smile. "If I could do that, what would I have to worry about? Every time I listen to their discussions about their action plans, I understand the contents but dare not anticipate the effect. Who knows what those rabid people are capable of next..."
"I don't know if you can understand, Doctor, but I always feel like we're fighting with our hands tied, yet the enemy can use all kinds of weapons and armament."
"This is not your illusion. Good people will always face this situation when dealing with bad ones. Therefore, I want to tell you the approach I take when facing this situation..."
"What's that? Can it really eliminate Hydra?" Peter asked curiously. He couldn't think of a way to deal with them besides facing them head-on.
Shiller chuckled, "I have a plan..."
As a result, Peter became another mole for Shiller inside the Avengers. Quite right, he even worked with Grant. Grant was responsible for causing a scene and attracting the Avengers outside, then leading them to the Hydra base nearby where the Winter Soldier was hidden.
After Captain America and Iron Man started to argue, Peter had to seize the opportunity, pretend to be injured, and it must seem to be by the Winter Soldier.
In short, it's the 'distress strategy', a way for diverting attention. Even if it came to the worst, it might still help to quell their heated argument.
People arguing in anger tend to say things they don't mean, escalating the fight till they fall out completely. One vigorous effort followed by a gradual decline can eventually exhaust them. However, once they exit this atmosphere, they'll have more time to calmly think about what caused everything.
Iron Man and Captain America are both intelligent. Even if they are momentarily blinded by emotions, as long as they take some time to think, none of them would want the situation to worsen.