The words in Group #1 are "not self-describing". That is, the word "cabbage" is not a cabbage, "French" is not French, and "monosyllabic" is not monosyllabic.
The words in Group #2 are self-describing. That is, the word "English" is English, and so on.
The words in Group #3 are those that don't seem to fit into either category, in a paradoxical way. The word "heterological" is a word coined to mean "different from its meaning". With this sense, "French" is heterlogical and "English" is not. Moreover, the words in Group #1 are heterlogical and the words in Group #2 are not.
But then where does the word "heterological" itself belong? It surely must belong in Group #1 or Group #2. It belongs in Group #1 if it is heterological, that is, if its name "heterological" does not correspond to its meaning, that is, if it is not heterological. Similarly, trying to decide if "heterological" belongs in Group #2 leads to contradictory results. So, to fudge things a bit, we stick it in its own paradoxical Group #3, which is for words which are both heterological and not heterological.