For CBC mode, the issue boils down to the fact that you cannot detect if a man in the middle modified the message. The data is still confidential, the man in the middle cannot read it without the key, but they can modify it, and it still would be decrypted at the recipient.
Ideally you want to ensure data integrity. For CBC mode in particular, you can perform the CBC byte-flipping attack. Lets assume a message is encrypted, and you know a single block. You can convert that block into any block you desire, because of how CBC chaining works. The plaintext of the next block is xor'd with the ciphertext of the previous block. So by altering the previous blocks ciphertext, you change the block that the plaintext decrypts to. Thus in exchange for getting one block to decrypt to gibberish, an attacker can control what the next block decrypts to. This is undesirable. Hence Authenticated modes such as CCM and GCM are used.
An example use-case of GCM mode when sending data over the internet between a client and a server, such as in TLS. You don't want CBC byte flipping to be a possibility. You want to ensure that the data you decrypt is in fact what the person at the other end sent to you.
Also to your point about encrypted hard-drives, being able to have evidence of any data tampering is a desirable property. CBC byte flipping attacks would only be evidenced by file corruption when looked at through its respective program. Its possible that the tampered file could be rendered as valid.