Many Chinese compound words are made up of two characters contain a similar meaning. In those cases, you can reverse the order of the compound words and the meaning would not change.
Both "痛" and "苦" has the meaning of "pain", And the standard compound word for "pain" is "痛苦". Since the two characters have the same meaning, it is acceptable to reverse the order and say "苦痛" instead. ("不堪苦痛" means the same as "不堪痛苦")
Both "冷" and "清" has the meaning of "unpopulated", And the standard compound word for "unpopulated" is 冷清. Since the two characters have the same meaning, it is acceptable to reverse the order and say "清冷" instead. ("埸面清冷" means the same as "埸面冷清")
Both "互" and "相" has the meaning of "mutually", And the standard compound word for "mutually" is "互相". Since the two character has the same meaning, it is acceptable to reverse the order and say 相互 instead. ("相互攻擊" means the same as "互相攻擊")
As for the reason for doing so? I think it is a way to showcase one's literary knowledge, make you sound more refine. You need to know which compound word is made up of two characters that have the same meaning. Less knowledgeable man may make a fool of himself by reversing the order of a wrong compound word. For example, saying "用信" instead of "信用", or saying "殺謀" instead of "謀殺" is unacceptable.
More example of common reversible compound words:
鬥爭 --> 爭鬥 (fight) e.g. 一場爭鬥 = 一場鬥爭 (a fight)
愛情 --> 情愛 (love) e.g. 一段情愛 = 一段愛情 (a romance)
空虛 --> 虛空 (empty) e.g. 內部虛空 = 內部空虛 (empty inside)
淒慘 --> 慘淒 (miserable) e.g. 慘淒下場 = 淒慘下場 (miserable end)
抗拒 --> 拒抗 (resist) e.g. 無法拒抗 = 無法抗拒 (cannot resist)
解辯 --> 辯解 (explain and defend) e.g. 無法辯解 = 無法解辯 (cannot explain and defend)
找尋 --> 尋找 (search) e.g. 尋找消失的國度 = 找尋消失的國度 (searching for the disappeared kingdom)
Since not all compound words are reversible, it is safer to just use the standard forms. Reverse the order only when you know it is acceptable for sure.
Notice: Some compound words with two characters having the opposite meaning can also be reversed. e.g. 不顧死生 = 不顧生死; 不論赢輸 = 不論輸赢