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?

In a sense, correlation is defined between more than two variables, through a correlation matrix.  This is not a single number of course, but that is only natural given that it is describing correlation between several pairs of variables.  This situation is analogous to many types of measurement in multivariate analysis, where we measure aspects of the behaviour by vectors or matrices.  You might also be interested to note that the correlation matrix for a set of variables is sufficient to compute the coefficient-of-determination for any Gaussian linear regression involving those variables (see this related answer), so even when we extend our analysis to look at conditional correlations, the correlation matrix is sufficient for this purpose.
Of course, even with a correlation matrix, it is merely describing the pairwise correlation between each pair of variables and resulting linear relationships conditional on other variables.  The reason these correlation values are for pairs of variables is that they are measuring the tendency for one thing to vary with respect to a second thing.
