Why are certain rules conversely repeated in associations results?

Association rules look for the co-occurrence between items, but they do not necessarily imply causality. So, for a rule like [tomatoes → lettuce], the inverse is also true [lettuce → tomatoes]. In other words, the presence of lettuce in a supermarket basket is not necessarily a consequence of buying tomatoes or vice versa. Rules tell us that both item sets are more likely to be bought together than separately, which cannot be interpreted because of one another.

You will also notice that rules with same items with inverted order have the same values for some association measures (also called symmetric measures) such as leverage, lift and support while others (asymmetric measures) are different, such as confidence and coverage.