This is because of being able to figure out the keystream for a given key and nonce when you can get both to be reused and the stream contains predictable information.
In many ciphers, a key is used to produce a series of ones and zeros that are xor'd with the data to produce an encrypted value. This string of ones and zeros is known as the keystream. If you are able to reuse a nonce and the keystream isn't altered based on the content of previous plaintext blocks, then you can look for known packets to appear in the content. When these known packets occur, you will see a predictable pattern occur and will be able to determine that you know that portion of the keystream.
By repeating the process, you eventually can gain more and more knowledge of the keystream and can then read or manipulate anything found on a known portion of the keystream. RC4 is EXTREMELY vulnerable to nonce reuse as it is a pure xor'd keystream. Similarly CTR modes of AES will be extremely susceptible. AES CBC-MAC will be a bit less impacted, however doing constant key resetting could potentially bypass the chaining due to always using the same set of initial blocks, so some information leakage would potentially still be possible, especially for the attacker faking a new client where racing will not be a factor.