Send them this article: http://www.joelonsoftware.com/articles/fog0000000069.html Then, send it to yourself.
There are legitimate reasons for a full rewrite. If, for instance, you can change the platform and do the rewrite significantly faster than the original technology and implement changes faster, then the rewrite may be the may to go. Imagine you have an app built on J2EE, with lots of logic on templates and no tests whatsoever. It's huge and maintaining it takes a huge effort. Every bug takes weeks to fix and generate…
"Imagine you can write an equivalent app in Ruby on Rails in two weeks, with tests."
You've already said that the existing app has "lots of logic" and is huge. Every bug takes weeks to fix, which means the "lots of logic" is seriously twisted up and not easy to decipher.
If that's the case -- figuring out the logic to fix one bug takes weeks, then it's inconceivable that you'll untangle all of the logic in two weeks. That's before you write a single line of Ruby -- if you want an "equivalent" app, that means you have to know what the current one does, first.
This is the usually-fatal flaw in the "rewrite" argument. The existing app needs to be rewritten because no one can understand it anymore (is is both poorly-written and very large/complex). But because no one can understand it anymore, it will be extremely difficult to rewrite, unless you work as if you were creating a new, similar application.
This is also why refactoring works. You cut off a bit of the existing app, figure out just that bit, write tests for it, and then replace just that bit with new code.
You can even refactor an app into a completely different language, actually -- you have two apps running parallel, and gradually move over bits of functionality from one to the other. In the process you'll need to gradually enforce order (and separation of concerns...) on the original app, but you need to do that either way.