One thing that has to be noted is that there is a certain anti-authoritarian central theme to most of Dr. Seuss's works. He himself admitted that he was 'subversive as hell' - as your own article notes. This, in the context of China's Cultural Revolution (the period when the book was banned), was a bad thing. Said Revolution aimed to exterminate the last vestiges of capitalism and Western influence from the Chinese sociopolitical landscape - in doing so increasing the power of Mao's central government in Beijing.

Therefore, a figure such as Seuss - despite by all accounts being on the left side of things politically - would have been understandably unpopular with the Chinese leadership. There appears to be relatively little concrete information out there on why this book in particular was banned rather than others - but I wouldn't be surprised if it were due to its popularity (the 4th bestselling English-language children's book of all time, after all). Ensuring the transmission of 'correct' orthodox communist doctrine to the young was also a key part of the Cultural Revolution - which may explain why the government would bother to bother such seemingly innocuous children's books.

I'd like to question the premise of the post. Is there any evidence that the said book was actually banned? The author of the linked article didn't seem to provide any source.