Yes, it's ok to not want to learn something. As a student, I never really warmed to acrobatics. Rolling, diving, cartwheels, handstands, I found it all unnecessary. But I chose to find something useful in the training, because the alternative is to either find nothing useful in the training, or to simply not go to class, and because I had that attitude I found a lot of good reasons for training acrobatics.
As an instructor, I teach a number of acrobatic maneuvers. Some of the very same ones I didn't like nearly so much as a student. Some I still don't care for personally, but that I recognize might be useful to the right student. The entire curriculum isn't there for me to like, it's there for the single purpose of transmitting knowledge of technique. Skill comes from practice.
I know there are parts of class my students don't like. PT, acrobatics, basics in the air, shadowboxing, point sparring, ground fighting, there's always something somebody doesn't like today. But it's my job as an instructor to teach good karate, and that's what I try to do. It's not for everybody.
It's ok to not like the drills, exercises, or practices of your instructors. Hopefully they are trying their best to convey good techniques every time they step on the training floor. If they aren't, you should probably leave and find a school where they are. But if you believe they are doing their best, and you believe in the quality of the material, then I would say give them the benefit of the doubt. Assume that as the expert that people pay to learn from, they may know what they are doing. I'm not saying it's a given, but it's likely that if they are standing at the front of the room, it's because they know the most about karate. Maybe there's a reason they do what they do.
Have you asked them? Maybe the things you don't like would be less off putting if the reason behind the method was clearly explained. I would be more suspect if they couldn't or wouldn't explain their method. That would imply to me that they were simply repeating the methods of their teachers without an underlying base of knowledge to support them.
As a student, I try to find something to learn in every lesson. As an instructor, I try to find something to teach with every student. I consider it a point of personal honor. The path to excellence is consistent action. Better today, better tomorrow. Nothing else matters. I know that to get there I have to train every day, and I know that for my students to get there they need to practice the drills and exercises I instruct with diligence. If they do, they'll have their own students some day. If they don't, or don't come to class, they'll never improve. But that's their decision. And mine is mine.
It's important to know for yourself why you train. If it is for self defense, you have to learn sticks. It is what it is. The lessons taught by sticks apply universally to weapons, both manufactured and improvisational, and while you don't have to become an escrima expert, you have to swing and dodge a stick from time to time to learn how to defend against one and with one. But maybe you don't want self defense. I'm really not presuming, people take martial arts for a lot of reasons. Decide what yours are and then talk to your instructor. If a student came to me and said they didn't want to learn sticks, we'd discuss it, and we'd find a way to move forward. Either I'd convince them to pick up the sticks for my reasons, or they'd convince me not to make them for theirs, and I'd give them something else equally useful to do while everyone else worked sticks. I certainly wouldn't kick them out of class, I want them to be there. Besides, there's ten thousand things to learn in martial arts and you'll never master them all. If a student wanted to practice spin kicking instead of sticks, or ground fighting instead of sparring, I could make that work. I want them to love their karate like I do, not resent it.
I think the answer always comes back to communication. Talk to your instructors. Talk to your fellow students. Talk to your training partners. If you don't, things can't ever, ever, improve. And if you can't, leave. Find a place that isn't ruled by fear. Life is too short and karate too easy to find. There's somebody in your area doing something awesome without all the BS. Is it you? I hope so.
As for swinging a stick with the wrist, I teach both ways. First, the students learn to keep the wrist locked and swing from the elbow using the whole arm as a lever, then, as the student advances, we begin to practice more sophisticated strikes, blocks, flourishes, and transfers using the wrist. Neither is inherently better or worse. The decision to use one technique in place of another is context specific and in real time occurs at a speed that's mostly beyond active cognitive ability. Your mind perceives stimulus and reacts with the appropriate trained response. At least, that's the goal. The stick is a lever. We swing levers all the time. Baseball bats, golf clubs, brooms, shovels, pens, even the bag of trash you swing over your shoulder. Do you always hold your wrist the same way in every circumstance?
If the issue is medical, either pain or physical inability due to age or injury, then of course I would never make a student perform that part of the material. I have students who can't fall or roll safely due to joint, bone, and back problems. Of course I'm not going to refuse to train them just because they can't perform Breakfall Set. No more than I would ask a man in a wheelchair to stand and walk or refuse to train him if he could not. Every man, woman, and child has the right to learn karate. My only two requirements are that they shower regularly and that their checks clear. And the second isn't my rule, it's the owners. If I could do it for free I would in a heartbeat.
I say trust your instructors. If you want to get where they've gotten, trust that they are leading you there. It would be truly vile if they were purposefully leading you astray, I hate to think that there are instructors who do that. If you can't perform the material, or decide not to, then speak to them. They are there for you. We get stronger. That's part of the training too. I was fat, out of breath, and weak when I began. I couldn't jump, I couldn't kick, I could barely keep my arms up during class. But karate made me strong. The things I couldn't do when I began are easy now. The things I still can't do are far more challenging, but I know the path to excellence now.
Take consistent action.
-Rob