Why is correlation only defined between two variables? I am an MBA student is taking statistics courses.
Our statistics prof was teaching us about correlations in statistics. We learned about Pearson's Correlation of Coefficient which is defined as the correlation between only two variables.
I am asked the prof if the correlation can be calculated between more than two variables and he said "no". But I am struggling to understand why this is the case?
For example: Hurricanes are correlated with Wind Speed, Hurricanes are also correlated with Temperature - Although I am not a meteorologist don't actually know if this is true (I just assumed this to show a point), we can see that in theory more than two variables can be correlated.
Therefore, why do we only evaluate the correlation between two variables and not more than two variables?

Such a statistic would be hard to define and interpret. Say you have the variables $A$, $B$, and $C$. The pairwise correlation between $A$ and $B$ is close to $+1$ and the pairwise correlation between $B$ and $C$ is close to $-1$. What should the single number correlation between the three variables be? High, low, or maybe zero?
You could instead look at correlation matrices between all the variables, but it is a highly overrated approach that could be misleading, and lead to a false sense of understanding. One example is people blindly dropping from their analysis variables that are strongly correlated with each other, or weekly correlated with the dependent variable, missing the point that those relations may change when controlling for other variables. It is like in the parable about the blind men and an elephant:

A group of blind men heard that a strange animal, called an elephant,
had been brought to the town, but none of them were aware of its shape
and form. Out of curiosity, they said: "We must inspect and know it by
touch, of which we are capable". So, they sought it out, and when they
found it they groped about it. The first person, whose hand landed on
the trunk, said, "This being is like a thick snake". For another one
whose hand reached its ear, it seemed like a kind of fan. As for
another person, whose hand was upon its leg, said, the elephant is a
pillar like a tree-trunk. The blind man who placed his hand upon its
side said the elephant, "is a wall". Another who felt its tail,
described it as a rope. The last felt its tusk, stating the elephant
is that which is hard, smooth and like a spear.

Looking at the pairwise relations tells you only the part of the story but is not enough to get the full picture right. We all hope that our brain would be able to somehow combine all the information for the full picture, but if that was the case that people can just eyeball the numbers to draw legitimate conclusions, we wouldn't need statistics.
For many variables, we use instead the multivariate models like linear regression or partial correlations that tell us about pairwise relations but corrected for the influence of other variables.
