Why do we use the term "uncorrelated" to describe linear dependence/independence? Terminologically, "uncorrelated" to me means that 2 things have no relationship, not necessarily constrained to linear relationships.
However, in statistics, we seem to confine "uncorrelated" to mean 2 things have no linear relationship, but could be related through other relationships. Why is this the convention? 
For example, consider $X$ to be a uniform distribution symmetric about $[-1,1]$ and $Y=X^2$, it can be easily shown that $cov(X,Y)=0$, which means $X$ and $Y$ are uncorrelated by the statistical definition, but the 2 variables are clearly related through a polynomial relationship. 
 A: "Correlation" has a technical definition, which is the one used in statistics. It usually refers to the Pearson product-moment correlation. Correlation is one measure of association; indeed, it is one of the simplest and most used measures of association, which is probably why it is used in common parlance when "association" is more technically accurate today (because it includes relationships not well described by the Pearson correlation). Your understanding, as you have explained it, of "uncorrelated" reflects this convention. It is possible that the common use of "correlated" precedes the statistical use, but that is a matter regarding the history and sociolinguistics of science on which I have no authority.
If you are engaged in statistical or scientific discourse where precision is important, you should change your understanding of the word "uncorrelated" to mean "having a Pearson correlation of zero" and use the word "unassociated" to represent the lack of a relationship, not just a linear relationship, between phenomena.
