Well, "never" is a strong word but I can't think of many situations where a single variable tells us much (maybe I'll post one example later). Sometimes, even two variables aren't enough.
Consider this article on Millennial employment. It has several "yes, but..." situations. The articles say "look at the relationship between two variables" and then goes on to say "yes, but when you add other variables you get different relationships."
Look - there's a gender gap in pay! That's two variables: gender an pay. Yes, but when you add in major the pay gap reduces significantly. When you add in taking time out for raising children, the pay gap reduces even further and reverses in some fields.
Look - graduates of for-profit schools make more money than graduates of non-for-profit schools! Again, two variables: school type and pay. Yes, but when you add in age and work experience, you find that younger, inexperienced for-profit graduates make less.
There's another on race and unemployment (I'll blow the surprise - Asians have the highest unemployment rate).
This article is a great example of the difficulty in attributing cause to relationships in two variables. It makes me wonder why introductory statistics classes focus so heavily on single variable methods. Most students take, at most, one statistics course. Maybe that course should spend more time on analyzing multivariate relationships.