Yep I do, not a flat out argument, but I'll get into a discussion about WHY she wants me to do something. I don't just 'do' something I need to know why. And sometimes I don't agree with what she wants me to do. My trainer is also a very good family friend and often asks me for MY opinion on how her horse is travelling and if I can sit and watch her ride him and let her know if I can see anything that she needs to change. So she is quite happy for me to question her teaching. 99% of the time what she wants me to do works very well. But I do find that because she also teaches beginners and has school horses to pay the bills, sometimes she will revert to beginner rider mode and dumb things down a little too much. At those times I need to give her a quick flick on the backside with the whip as I ride past haha!
I think the competition between us and our different ideas helps both of us out as far as teaching and learning goes. I also LOVE proving her wrong haha, she lives to be right, and so proving her wrong feels so satisfying :P For instance when I got Hugo, the first week there he was travelling well, but wanted to stay up in an elementary frame when he wouldn't even be able to get through a prelim, being straight off the track. Coach said draw reins would get him travelling softer in a week rather than spending months sending him forward and into the bridle to get the same result. Well I went home, spent the week working in the paddock on him up and down hills and making him reach for the ground. Brought him back a week later and he travelled around with his nose on the ground stretching from the wither and over tracking.
You have to remember that yes, coaches are there to help you and obviously they've got more experience than you. But YOU are the only one that really knows your horse. and if something doesn't feel right, and you know you can get what the coach wants you to do but with a different method, speak up! On the other side, if you don't know how to get what the coach is asking for, listen to them and persist even if it feels like hell, because speaking from experience, it's often a case of riding through the rough patch and suddenly it will click and you'll be amazed at how your horse is travelling ;)