My first jobs as a trainer were at a university, and I've always approached training with the goal of not only creating physical adaptations, but also increasing understanding of the body and movement. I'm pretty pedantic, and I will spend an annoying amount of time breaking down a squat or plank because my goal is to make people their own trainer. I want to foster a body awareness that allows us to move without a set of eyes on us. When I first started working at private studios, I found that the emphasis was often on entertainment (not that I have a problem with that--fun is important), but that instructors often were hesitant to spend too much time teaching because they didn't want to frustrate their clients.
Which is understandable. We are in the service industry, but by allowing someone to run rampant with a crappy form, we are being lazy and timid. We are creating a workout, but we are not training. I took a class this week where the instructor wrote kettlebell swings on the board but did not even demonstrate a kettlebell swing before asking us to do it. Nor did she give us a hint about a reasonable weight for the exercise. I get where she was coming from--she wants to pack as much as possible into a class, and if she took the time to teach us, she would lose precious sweaty seconds and maybe lose her studio's reputation as one of the most intense workouts. But it's crap. If you want to repeatedly slam your body full speed into the wall and get a little skinnier and more toned, then that's working out. But if you want to train, you have to get your brain and body on the same team. You have to take the time to learn technique. And here's what you'll get out of that: you will advance in ability (lat pulldowns will lead to pull ups...etc.), you will develop greater body awareness (which means that you will know when you need to rest and when you can work harder), you will avoid injury because you will understand yourself better, and finally, you will be able to translate your strength into the rest of your life. If you take random classes that are really hard at random studios, you are likely enforcing negative movement patterns and even amplifying issues. But if you take the time to learn how to properly squat, you are becoming mindful of your movement and you might notice that you are rounding your spine next time you sit down. You become your own trainer.
If your trainer is "slowing you down" and you become frustrated with their coaching, look at it long term. Do you want to train or do you want to workout? If you just came to sweat as much as possible with no thought of the future, find classes where you get ignored. If you want to learn, find a coach who has opinions about your movement and tips to help you. It's better to be told to lift your head up 500 times than to allow your poor alignment to create all the pain and tension in your neck. Embrace learning.