In the wild angelsfish school. It may be to be secure in finding a nate or as a defensive behavior. But we need to remember that the wild does not have glass/acrylic walls and is at least a wee bit larger than our home aquaria. So, to elicit natural behavior we need massively larger aquaria.
From that logic it would seem rather obvious that aquaria fish behavior is not natural in most cases. Nevertheless, freshwater fish are quite adaptable. They tolerate differing water conditions, neglect, and us. Given all this there is one natural instinct that still survives, the will to reproduce. This is a social behavior even when they exclude all tankmates.
Since our fish are, for the most part, many generations from the wild and have never seen a National Geographic special, they will behave in ways that are appropriate for their world. Loneliness is a human emotion and we risk error in trying to tie our emotions to animals. So, while a lone angel may look for a companion we cannot call it lonely or depressed. It is just acting appropriately to its world. This could vary with wild caught specimens but the word to use would be stress.
I know I tend to ramble, but you get my point.
Charlie