Pope's "The Rape of the Lock" is a mock-epic, which means it is written to be funny. Humor works by using overstatement, surprise, and exaggeration: We as readers are so startled by the over-the-top outrageousness presented that we laugh.
Pope needs to use the grandest and most elevated language possible as a contrast to the petty nature of his subject, which is the fact that the Baron has caused massive outrage by cutting a lock of his beloved Belinda's hair off without her permission. We might call this situation the original "First World" problem. Just as today a writer on a sitcom might raise laughs by using exaggerated language to equate a character breaking a fingernail with a geopolitical crisis, so does Pope with the hair cutting.
Pope uses a crisis in the Ancient world as his contrast to Belinda's shorn lock: the Trojan war. Pope imitates the poet Homer's heightened language in writing about this war in his epic, the Iliad. While Homer uses emotive language to write about what really was a serious and tragic affair, Pope hijacks that language to describe a completely trivial event in which nobody really suffered. What can anyone do but laugh and think how silly it is to get so upset over a lock of hair when the exaggerated language used to describe it is that of gods, epic battles, rapes, enslavements, and truly tragic deaths, including Hector's infant son being thrown off a parapet? Pope wanted people to realize how ridiculous this hair cutting was—which, in real life, caused a feud between two wealthy Catholic families in England—and the slippage between the language he used and the event helped him to be successful.