Why did Captain Cold decide to call out Flash in public in "Revenge of the Rogues"?

In the 1x10 ("Revenge of the Rogues") for The Flash, Captain Cold teams up with Heat Wave and wreck havoc on Central City. There is a lot of conflict as Captain Cold is calling the shots while withholding information from Heat Wave (to the point of stupidity, I think, but that's a different matter).

However, I can't figure out why they decided to call out Flash in public at the end. At first, they break in to some places and hope that Flash will come to stop them. It's private and they don't have to reveal their identity.

By the end, they decide to call out Flash in public and reveal their identities. When their plan fails, Captain Cold laments that the public having irrefutable proof that Flash exists "changes the plan".

Why is he surprised by this? Of course people know that the Flash exists because they called him out in public! It seems to me like they tried to keep Flash (and their identities) a secret, then did a 180 on that and called him out in public, then lamented the fact that he was no longer a secret.

Am I missing something?