How does encrypt-then-MAC protect from CCA?
What CCA basically means is that attacker supplies for decryption any ciphertext he/she wants and observes the reaction of the system. This reaction can be used to infer information about plaintext/key. Many dangerous attacks are based on changing some bits in the ciphertext and observing how when and how the system fails. This is often enough to partially or fully recover plaintext or key. What authenticated encryption (particularly encrypt-then-mac approach) basically does is prevent attackers from being able to change ciphertext. Doing so requires recomputing of mac, which by definition can't be done without knowing the mac key, otherwise decryption immediately fails due to incorrect mac, and as the system doesn't know anything about the plaintext at this point, the attacker can't possibly learn anything too.

Attacker's own application is useless in this case, as without the key itself any decryption failure just points to one and only obvious reason - wrong key.