The simplest way to think about it is during the receiving process: checking the MAC before decrypting catches and rejects evil messages earlier so there are fewer things that can (and will) go wrong. Even if you tell the world that the message wasn't invalid, you don't reveal any new information to the attacker.
OTOH, if the receiver must decrypt before checking the MAC, any information leaked to the attacker (success or failure, timing, etc) is very likely to give the attacker a systematic method to decrypt some or all of your secret plaintext.
OTOH, if the receiver must decrypt before checking the MAC, any information leaked to the attacker (success or failure, timing, etc) is very likely to give the attacker a systematic method to decrypt some or all of your secret plaintext.