With absolutely no disrespect to your sensei or others who share the same view, I'm not sure I agree with that stance on the issue. It just doesn't seem practical.
No one in our dojo ever uses the words 'sempai' or 'kohai', but the roles do exist. We seem to treat it more as a combination of experience and [perhaps more importantly] sincerity.
There are some people who helped me when I started who fulfilled the role of sempai, and now my ability has meant that I've effectively become their sempai.
But, like I said, it's not at all stressed or implied in our dojo, but if you sit down and look at it there is sometimes a sempai/kohai thing going on.
Moreover, I agree with Ron -- the terms are too loaded. It'd be far easier to just train