Basic Men Uchi
I'm sorry for asking such an elementary question in here, but it's been a long time since I practiced my basics... For a basic men uchi, we move the shinai up with our right hand and then strike down with our left?
Don't be sorry. I appreciate your question.
I don't think you meant lifting up with the right hand only and striking with the left hand only. Correct?
I know what you mean though. Probably you heard this when you learned the basics. Or you might have mixed up teachings. In the basics, you have to use your hands equally.
There is a tendency that many beginners use their right hand a lot more than they use their left hand. This means that they are developing a bad habit and will have a hard time to learn new techniques.
So instead of thinking how you should move your hands, you should concentrate more on "moving your swords straight up and down in a good posture". While you are doing so, you should remain relaxed.
Hope this helps. If you have more questions regarding this, please don't hesitate ask.