Counterpoint: 1 a : one or more independent melodies added above or below a given melody b : the combination of two or more independent melodies into a single harmonic texture in which each retains its linear character : polyphony 2 a : a complementing or contrasting item : opposite b : use of contrast or interplay of elements in a work of art (as a drama)
Counterpart: 1 : one of two corresponding copies of a legal instrument : duplicate 2 a : a thing that fits another perfectly b : something that completes : complement 3 a : one remarkably similar to another b : one having the same function or characteristics as another
When I wrote an earlier question I used the word "counterpart" to define "On the other hand" in reference to "On one hand", but, in their answers to the question, competent speakers of English language called the former "counterpoint", not "counterpart".
After having verified on Merriam Webster Dictionary Online, I cannot still understand the reason why I should use "counterpoint", rather than "counterpart".
Can anybody explain why "counterpoint" is proper English, while "counterpart" is not?