I don't follow your logic. Not saying it is wrong--just that I don't follow (and I have been around too long to confuse those two!)
So maybe the next step, once tag is eliminated, is to re-do the letter frequency. It was, and now is:
cat 142 cat 131
dog 212 dog 211
has 141 has 131
max 241 max 231
dim 212 dim 212
Now we can eliminate cat and has since their frequency counts are the same.
I don't understand why that lets you eliminate these two. Wouldn't the same argument be used to eliminate dog and dim in step 1, since they also have the same frequency counts initially?