From afar it may seem that Clint, the older and more experienced Hawkeye acts as a mentor to Kate. In some ways this is true. He teaches her his best tricks, about all of his trick arrows, and from time to time gives her some wise advice. Mostly she's the one helping him. Kate is independent and knows what she wants from the world despite her young age. Compared to that Clint Barton, a hero who has spent his whole life working along super-powered friends, is a hot mess.
Despite their mutual respect for one another Kate can only have so much patience for Clint's shortcomings. She makes an effort to help him out on his solo missions when she can. She often uses her family's name to get him access to a target or saves him when things go wrong. She even makes an effort to encourage him and remind him why he's fighting when he gets low. That being said, there is only so much she can take and when he shuts her out she's not willing to deal with being mistreated. Kate's frustration with Clint's inability to communicate and dismissal every time she tried to help him was the primary reason for her decision to head for the west coast. Kate had cleaned up after a number of his messes and was fed up when he didn't make the effort to help her.
In the end though, Kate and Clint are good friends even when they fight. Despite all of his shortcomings, she looks up to him. Clint saved Kate as a member of The Avengers when she was a child and taught her what it meant to be a hero. It's just a matter of returning the favor when he forgets why he's consistently been a member of The Avengers since he initially joined.