China considers Taiwan to be a part of China. This goes way back to a long standing rivalry. The communist party of China and the KMT fought for power in China, the CPC won and the KMT became an impotent exile government in Taiwan that for a very long time declared to be datruetrue government of a larger China which consisted of the Chinese mainland and Taiwan. The KMT has lost this battle and the government position in Taiwan since then, and officially Taiwan is considered to be something like an autonomous region in China. Unofficially Taiwan is still treated like a mostly sovereign country.
When Japan talks about defending Taiwan, that would be like Mexico saying it intends to defend Texas against the US government, in case Texas wanted to revamp the Confederacy. The comparison is bad but the US would understand such a statement like Mexico threatening to declare war against the US. And that is exactly how China sees the Japanese statements about defending Taiwan.
If you consider the History between Japan an China, where preWW2 imperial Japan was ruthlessly occupying big parts of China for the better part of a century, it's very unsurprising that Chinese officials might have let say "rude reactions" to potential Japanese "involvement".
The other part is that Japan was on the loosing side of WW2 and conditions for it's surrender was that Japan wasn't allowed to engage in warfare. China was part of the winning side and technically China could treat this as Japan violating the conditions of their surrender in WW2.
Regardless where you stand on the Taiwan question, Japanese officials are morons of the highest order for spraying gasoline on the fire, they are not making China rethink it's position on Taiwan, they are making China rethink it's military positions towards Japan. All they did is poison diplomatic relations.