Because you can trade some form of mean reversion. If relationship deviates from historical correlation, then you place a bet it will reverse itself. (You can phrase that in other ways.... I.e. if A and B are usually correlated and A goes up, then you think B will "follow".) You can also have auto-correlation, meaning correlation between now and previous time series.... Aka straight trend following or mean-reversion on price.
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To add how they put it in the course, it helps figure out how diversified you portfolio is when you have many holdings on at one time. If everything is perfectly correlated, there is no diversification, and it's very high risk because they all move in the same direction at the same time. The goal (as presented in the course) is to get holdings with very low correlations for higher diversification. This reduces risk because some holdings may go up, some may go down, and some may go sideways, then depending on the weighting of the holdings, hopefully you have picked the right combination so on average the portfolio does not swing up and down too wildly.
That's actually a different topic, although the standard reason why correlation is studied. It's the core of modern portfolio theory. If you look at the expected return of a portfolio (or any random variable), it's just the weighted expected return of each instrument of the portfolio. So, diversifying across instruments, if all have same expected returns, doesn't hurt your portfolio returns. The expected variance of a portfolio (or sum of any two random variables) is different. It is equal to variance of each instrument + a covariance term (2 x correlation x std deviation of each). By making correlation less than 1, you immediately drop portfolio variance. And therefore, same returns for lower risk. But this doesn't seem to apply to what you are looking at.... Finding correlation at different time periods doesn't help "diversify".