What adjective would subtly state that an argument is cheap, weak or insignificant?

Solution 1:

Your demand for a "not so loud word" makes me think of - tenuous.

If something is tenuous it's thin, either literally or metaphorically. Tenuous comes from the Latin word tenuis, for thin, and is related to our word tender. (vocabulary.com)

Tenuous arguments won't win any debate tournaments.

Usage examples.....

Solution 2:

Insubstantial (MW), inadequate, implausible, dissuasive, impotent. I suppose it depends on how polite you are trying to be. Hope this helps.

insubstantial Merriam Webster

: not large or important

: not strong or solid

: not real : not made of a real substance

Solution 3:

A tangential argument

(formal) having only a slight or indirect connection with something

Oxford Learner's Dictionaries

Also, sometimes one can clearly express polite incredulity, and get away with it, by using the word interesting.

Solution 4:

This may be less likely to cause offense, since it doesn't address the quality of the argument as much as it says what was in the argument wasn't enough.

insufficient