One of the goals of MAC is to detect/avoid message tampering.
Bellare, Canetti and Krawczyk defined 1996 formally: "The adversary sees a sequence $(m_1,a_1),(m_2,a_2),\dots,(m_q,a_q)$ of pairs of messages and tags ... and breaks MAC if she can find $m$ not included among $m_1,m_2,\dots,m_q$" and the corresponding valid tag $a = MAC_k(m)$.
However, you can not fulfill that requirement, as you can easily modify an message by adding additional blocks of all 0 at any position. Even worse, you can add a number of arbitrary blocks, as long as their total XOR results in all 0.
Thus, you can take a message/tag pair $(m_1,a_1)$, and modify the message to $m_2$. The formal definition does not require the tag to be new, pair of $(m_2,a_1)$ is a valid forgery.