I am practicing ballroom and latin dances for year and a half now with the great will to compete some day. The main problem with me is that I didn't have a partner and from two months a dance with a man who had never danced at all and started training by chance. He is a real tragedy, he cannot move at all and for me it is a real terror to waste my time trying to explain to him how to relax and get rid of his tension.
I need advice. Should I tell him that I don't want to dance with him anymore and try to develop myself without a partner, or what?
And how to do my best in training without a partner??

He may become a better partner some day. YOU may become a better partner someday, too. Meanwhile, practice alone as much as possible whether or not your keep this partner. I know all the talk is constantly about finding, getting, or keeping a partner. Admittedly, it IS partner dancing. But the more comfortable you become with your own part, the less you will rely on your partner in some ways. Some of your very best improvements can come from this solitary practice. You'll become much more able to adapt to anything a partner throws at you when you have to spend less time worrying about what you yourself are doing.

I believe in the catch-22 of dance but I would like to add something to it. One of the biggest problems that I see with finding partners is that everybody wants a better partner. I have seen it alot. This person does not like their current partner and wants somebody better than themselves. Partners are meant to grow together with their learning and do not over estimate the power of practicing by your self together. My partner and I do that all the time and then when we are together it flows that much better.