The sentence is
Variability in data is considered a nuisance.
Variability in data are considered a nuisance.
Initially I thought
is was the correct one, but it was corrected to be
are. I want to know the reason.
The first one is correct, and the second is incorrect. "Variability in data" is singular, and "is" is the correct form for singular, not "are".
Your second question, why someone else wanted you to use "are", can only be answered by that person, I think.