When Natasha told him that he was going to be a father, Clint was scared. At first he didn't know what to think. His own father was an abusive, drunk jackass who made Clint's life living hell.
So he tried to be in deniel for as long as he could.
But then one day Natasha's stomach was showing and sometime afterwards he felt the baby kick as a response to his voice.
Clint knew suddenly that all this was happening.
After Jeremy was born, and Clint held him for the first time, he realised how complete he felt. The only other time he felt like this was on his and Nat's wedding day.
So while looking down at his son who looked so much like him, Clint made a promise to himself that he would be a better dad than his own was.
He vowed to always keep his son happy.