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I see no harm in using well established mathematical terms -- dependent
and independent variable -- in particular contexts.
Yes, objects do not
explain objects and variables do not explain variables.
Explanations
are logical chains of cause-and-effect created by humans. A statement
like "too much fat in what you eat explains your overweight" is a
shortcut. A doctor is saying that an acceptable cause-and-effect chain
can be established between the diet and the overweight. The same is
true for a statement "more rapid loss of potential difference, between
two initially-charged plates, is caused by humidity."
In this case
humidity is the cause (in an explanation) while the time after which
one half of the charge is lost is the effect. What kind of harm might
result from saying that, in this context, humidity is the independent,
or explanatory, variable while the half-discharge time is dependent, or
response, variable? One may argue about validity of some explanations.
But it would be difficult to argue that attempts to explain reality are
not useful. That is the essence of what we do physics.