This is not true. Re-read the announcement and prior posts from Geocaching HQ Lackeys.
The announcement reads: "For those who currently have the app, it will be supported at least through June 2016." Nothing Lackey has said explains what "not supported" looks like beyond that date. It could mean all links and access to the web database will continue indefinitely we just won't fix bugs or add features (which they didn't do anyway) or it could mean well we can't take it off your phone, but don't expect it to continue to have access to our database systems but if you have saved caches you can still probably get some use out of it.
Don't get me wrong, I like the new app (and I like that as a Premium member I can use it on my iPhone or Android device without having to buy separate copies). I like the look and feel and I think that Groundspeak had let the classic app become dated, rarely fixed bugs nor offed new features (leading others to use c:geo etc.). I get that they need to focus on leveraging their data (and the wide availability of GPS enabled smartphones) to get more Premium members. I think this new app is a significant move in the right direction. I hope they are seriously interested in really developing it to have everything the classic app had and more (user stats as just one example).
As others have said, I think this would go better if members were drawn to the new apps exciting additional features rather than like me (and others) learning about this by seeing an update app notice from Apple saying we are changing its name as we are phasing it out for this new thing that (by comparison) is not yet ready for prime-time. But I like the direction this is going. Not sure I'll like a (likely) increase in the annual fee, but to see them really upgrade what for most players is the primary front door, this is a good thing
How about while your at it Groundspeak, doing an update to a very dated website too... On second thought, maybe you better wait till the app transition is first class before messing with the web interface.