Why is ECB mode unsafe if the key is kept secret?

this is my first post so I apologise if the formatting of my post isn't perfect.

I should start off by saying that this post is not for any malicious intent, rather for curiosity and understanding AES encryption/decryption.

I have been doing research about AES encryption and everywhere says that ECB mode should never been used and often refers to the famous Linux Tux penguin example. I understand that the vulnerability lies in the fact that a block of plaintext will always produce the same block of cipher text with some key.

However, I am new to this topic and I am struggling to understand the vulnerability in the following situation:

Consider a plaintext (P1) that is encrypted using AES-ECB to produce an encrypted ciphertext C1 with a key unknown to me. If I had another cipher text (C2) that was encrypted using AES-ECB (using the same unknown key), how could I obtain the corresponding plaintext (P2) even if I have P1 and C1 accessible to me?

My confusion lies in the fact that despite having access to P1, C1, and C2 — I do not know the key.

The issue with ECB is precisely what you've described in your question. Abstractly, the "encrypted" penguin doesn't tell you what the original penguin was but tells you quite a lot about the original message. This is very undesirable for an encryption scheme since revealing "some" information on the underlying plaintext can be enough to recover the whole plaintext.

Why not define security as obtaining the plaintext? Defining security this way is tempting but can lead to stating "obviously" insecure designs as secure. For instance, take a secure encryption scheme called AES-SEC, and modify it slightly (obtaining AES-SEC*) such that encryption works the same but also outputs a few bits of the original message. In this definition, AES-SEC* is secure, but it's not hard to see that AES-SEC* is insecure in many cases.

The ECB mode is "secure" if the plaintext contains blocks that are all distinct, which greatly restricts the practicality of ECB.

The basic security notion for an encryption scheme is usually that of "indistinguishability under chosen plaintext attacks" or IND-CPA. See this answer for an introduction to these notions. See also the Joy of Cryptography for an extensive discussion.