flaw in perfect secrecy of shift cipher? Why do we say shift cipher is perfectly secure when it is easy to break it (source)?
Let's say I have a plaintext.
"Australia is a big country";
I encrypt it using a shift of 2;
That ciphertext can be broken using brute force search over 26 numbers.
What you're referring to with "using a shift of 2" is in fact called a Caesar cipher and is not secure. You correctly pointed out, that it can easily be broken if you brute force the 26 possibilities.

But what the author is referring to is a so-called one-time pad (as described on page 78). It has the property of information-theoretic security.

The caesar-cipher can easily be brute forced to the original message, but on the other hand, OTP can be decrypted to any message of the same length. If we don't know any information about the message space then all keys are probable.