Hi Sarah
It is to have a smaller number of larger, high quality fruit, on plants that are trained vertically. If the sideshoots were left, a mass of leaves and stems would grow many smaller fruit and with more mildew on leaves. Maybe you should try one to see!
Cucumber plants on the ground do not need sideshooting…
Melons are different and after all sideshoots are removed from about the first three feet of stem, they need leaving to allow fruit to develop at the first node of each sideshoot (unlike cucumber fruits which grow out of the main stem). It is explained more fully in my Organic Gardening book.