Coaching call with client/feeling righteous

I had a session with a client today, my own self coaching at the end of the day revealed this model:

C: Coaching call with client today
T: My way of doing things is better
F: Righteous

A: Bully the client into agreeing with me
A: Try to explain tactfully to the client that I’m right and she’s wrong and she should do things my way
A: Become frustrated when she disagrees with me/I perceive her as being resistant to my ideas/being generally stubborn (could this be a separate model?)
A: Not teaching from compassion, curiosity, and love
A: Coach in more of an authoritarian/textbook angry style
A: Appear to be actively listening to her nodding my head so she feels heard and listened to, but secretly I’m not listening hard, I’m distracted with my own thoughts about how to explain things better to her so that she will agree with me and more or less say she’s wrong/doing it wrong

R: I don’t get to the root of the client’s issue. (I feel like this is a true result from this model but it doesn’t prove the thought)
R: I get the client to agree with me (because I basically bully her) (also, this includes another person, so not sure if this result is true either)
R: I create a false sense of my good coaching abilities?

I need some help with the results of this model, and if this is multiple models mixed together?

I would love to see what’s really going on here so I can work on dropping this expectation of my client and future clients because all I can see is bad coaching stemming from what I previously (unconsciously) believed to be a helpful thought. Ultimately, getting the client to agree with me doesn’t ultimately help the client solve her problem, if anything, it stalls progress on her goals because we’re not getting to the root of her issues, only reinforcing my cocky belief that I’m right and she’s wrong.

Would love some insight. Thanks coaches!