Suppose $H$ is a hash function; why is $H(k\mathbin\|H(k\mathbin\|m))$$$H(k\mathbin\|H(k\mathbin\|m))$$ not secure?
See this HMAC definition. In there, indeed two keys are used and the mac algorithm is $H(k_1\mathbin\|H(k_2\mathbin\|m))$ .$$H(k_1\mathbin\|H(k_2\mathbin\|m)).$$ Why don't we use $H(k\mathbin\|H(k\mathbin\|m))$,$$H(k\mathbin\|H(k\mathbin\|m)),$$ which has only one key?