I don't think it is a matter of "why change," but rather, "why consider." Furthermore, it is a waste of your time to convert. Instead, you should focus more on "spreading the word."
The best goal should be one of simple enlightenment, and in this situation it means getting someone to consider what is new and cool about <insert-your-language-here>.
For me, I tend to look at new languages when there is some particular idea I get excited about. In my case it is more about implementing an idea to test rather than building the next killer app. So, when thinking about implementing the idea about which I am currently excited, I consider what language/features I might use in order to realize my idea in the most informative and enjoyable way.
For example, there have been times recently that I've wanted to learn Erlang simply because it is my understanding that it would allow me to implement a distributed algorithm in the most direct way possible. I've implemented these sorts of things using Perl in the past successfully, but for this particular exercise I'd rather not have to manually simulate (in serial) many distributed nodes doing their own thing. This is no knock against Perl, but an example of what would compel me to try Erlang.
That example aside, I tend to always look at Perl first. This includes an investigation of the new features offered by Perl 5.10 and Perl 6. Now, as an admitted fan of Perl, I am going to be looking at the features of Perl 6 to see what things they inspire me to do.
I have the advantage of not being driven by projects that are dictated to me, but I understand this isn't the case for most.
So, to finally answer you question directly I would say that in order to whet another's appetite about something you're excited about, you need to know what kind of problems get them excited. Once you do this, it should be pretty easy to point out the new and exciting features that they might be able to take advantage of.
In the case of Perl 6, I think that you can take anyone interested in the following topics and convince them to take a look at the language and what it (or even Parrot) can offer: concurrent/parallel/distributed apps, functional/higher order programming, compiler writing, virtual machines, oop, etc.
As an aside, if Perl had a way to easily implement the type of environment that Erlang purports, I'd jump into that head first and forget I even heard about Er...what's it called again?