If one editor moves it from one catagory to another. Why should we have to wait until that editor reviews it.
Because not all editors have permissions to edit in all categories. In a perfect world, an editor moving a site from one category to another has permissions in both, and can do both the remove and the add. It does not happen that way alal the time, and this is, unfortunately, one of those times.
The site has been in the directory for more than 5 years. So far it has been more than 6 weeks waiting to be reviewed.
Yes, and that is how the sytem works. Since there is no "line" there is no head o the line that one can be moved to. However, an internal change will work to your benefit. Sites move from one category to another by an editor are separated from the rest of the submission pool, and while I cannot speak for othe editors, I am not changing my work habits to make a point of looking at those first. Unfortunately, your mileage may vary.
What happens if the editor of the new catoragory decides that the site is not appropriate after 2 years of waiting. Then i am out of DMOZ? While my competitors are in Dmoz.
Yes, that is always a risk. It is a risk that every site faces every time an editor looks through a given category. This is why we always stress the need to add unique content. When the directory was first being built a lot of sites were added that would not pass muster today, and periodically editors go in an weed them out. Sites get moved, descriptions get changed, sites get removed. That is the dynamic of a live directory at work.