Your app would have a nice geeky audience of tech nerds who would drool over how secure it is and how smart they are.
WhatsApp on the other hand "just works." It requires zero setup, zero technical understanding, and is available on almost every platform (at least the "biggies" anyway).
I would say its audience is teenagers, and the less tech savvy consumer in general. I cannot see them wanting to switch to something else unless you make come up with a USP which appeals to them (i.e. security is not a USP that they're interested in).
That said, I think the number of people concerned with message privacy is on the rise around the world. Over a few years, the market may grow significantly as privacy receives more attention.
I imagine a messaging app which works like TextSecure (as far as encryption goes), but integrates with Orbot (Tor for Android). Both phones would set up a Hidden Service so they can communicate directly, over the Tor network, over the Internet without an intermediate server.
That would be the perfect messaging system IMO. Not only would the message content be hidden, but who is talking to who, and when, would also be hidden. And it wouldn't require anyone to run a server to handle the messages either.
Please, somebody make this app.
What would change your thoughts regarding a secure messaging system? Open source?
Also, Skype's protocol and entire stack is entirely opaque and thus hasn't been nearly as checked for security issues as something like XMPP with SSL for example.