Because he was angry. All the Israelites gathered and fought the benjamintes, and destroyed the city, and killed ask the women. They also promised never to let their daughters marry a benaminite.

However, then some smart people realized they actually needed all 12 tribes so that encouraged the remaining benaminites to kidnap some women to marry. This saved them from extinction but it the tribe always stayed small.

The Levite and his concubine (could have been a lesser wife since polygamy was allowed and her father supported the relationship) were staying with an elderly man in Gibeah. The men of the town came to the house and demanded the old man give them his male guests (the Levite and his servant) to sexually abuse. He wouldn't but tossed out his virgin daughter and the concubine instead. The Levite sends parts of his concubine to the tribes to shake them up out of their moral lassitude. (But let's not ignore the fact he himself did this despicable, reprehensible thing himself in allowing a woman in his care to be abused like this.)

To send a visceral, grisly message about the Benjaminites' crime. He could say what they did in a letter, but that doesn't have the same impact without a visual aid. And since it was several thousand years before the first camera...