This answer is on my poor understanding of canonical correlations. It is not based on mathematical properties but on general observations I find that make canonical correlations interesting.
Because ordinary correlation has several problems:
- It compares two variables without taking into account the other variables
To overcome this one could use partial correlations, but then we run into the second problem:
- There are too many to make sense of the data
When canonical correlation analysis is used you have 40 or thousand of variables, and even if you had few variables and you could make sense of the partial correlations of each block there's another problem:
- It only considers two variables without taking into account the relationship of the others with their block of variables
If in partial correlations you give all the other variables expect the two you are considering you are assuming all are equally important and you are not considering the relationship between them.
And if you don't give the the variables of one of the block you are not considering their effect on one of the variables you are attempting to correlate.