Well... I've always taught by my sensei that to only use the left hand all the time...
Kendo-Guide.Com: It is an expression. It does not matter if people are right handed or left handed, when they strike in kendo, the right hand takes over the control of shinai.
That is why the kendo instructors always say, "use your left hand" or "use 'only' left hand", meaning, you have too much power in your right hand so use the left hand more!
Hope this helps to understand what your sensei is trying to tell you.