I'm right-handed, but now I can hold the shinai with one hand (either right or left), as I'm doing nito ryu kendo.
You left-handed people have the ADVANTAGE to it, because it will be used in Jodan-no-Kamae or nito-ryu, as there's a way to attack other opponents with different stances and hit the datotsu-bui as fast as possible.
It has the advantage to have the shinai under more control and attack faster than the weak hand.
I tried jodan-no-kamae myself alone with my weak hand and as a result it became stronger after strict training with the help of the right hand. :)
Kendo-Guide.Com: Thanks for sharing your opinion! Since I don't know what grade you hold and also I must mention this as one of the purposes of this website, no beginners should try jodan or nito.
Jodan and nito are for more experienced kednoists not for beginners. Unless you have a good teacher to teach you jodan or nito, you should be well trained in chudan first.