Why is ECBC-MAC with one key insecure?
Note that re-encrypting the output of CBC-MAC with the same key as it was calculated with is equivalent to appending a single all-zero cipher block to the message:
$$E_K(\text{CBC-MAC}_K(m)) = E_K(\text{CBC-MAC}_K(m) \oplus 0^b) = \text{CBC-MAC}_K(m \,\|\, 0^b),$$
where $0^b$ represents a $b$-bit block of all zero bits and $b$ is the block size of the cipher.

Thus, the classic attack on unmodified CBC-MAC with variable-length messages can be easily adapted to your scheme.  Specifically, let $$\begin{aligned} t\phantom{'} &amp;= E_K(\text{CBC-MAC}_K(m)), \\ t' &amp;= E_K(\text{CBC-MAC}_K(m')), \end{aligned}$$ and construct the message $m'' = m \,\|\, 0^b \,\|\, (t \oplus m')$, where $t \oplus m'$ represents $m'$ modified by XORing its first block with $t$.  Then $$E_K(\text{CBC-MAC}_K(m'')) = E_K(\text{CBC-MAC}_K(m')) = t'.$$