If Clint hadn't touched him then maybe Steve could have continued speaking rationally. No one was yelling here but Clint. But that shove couldn't be tolerated, and with a pointed look Steve shoved him back.
"No one is yelling, Hawkeye. Now you need to stand down and stop pushing this. Either you can help us relocate these people, or you can sit yourself down and have a time out until you're prepared to be an adult."
Steve responded to Wanda's look with a flat, and serious one of his own. He wasn't going to change his stance. "If you don't want do your jobs any more then go plan the best way to get him out. But do not presume to tell me I don't care. We are Avengers. This is what we do. Nothing has changed."