Essay
If you kill a beaver at its home and its family, a new beaver family will come back and either rebuild a dam or live there. This will create a cycle of killing beaver after beaver. If you move a beaver nonlethal and take other precautions, this will not happen. There have been ways people have tried to blow up beaver dams, but this leads to beavers rebuilding their dams or moving away up or downstream, and it disburses nature.
https://www.humanesociety.org/resources/what-do-about-beavers
Beavers also control floods by slowing the flow of water. This helps many animals by preventing their habitats or homes from being flooded. This also helps people because if someone were to have things near a stream and it gets flooded away that's bad but if theirs beavers to slow it down it's all good.
https://awionline.org/content/coexisting-beavers
Beavers also create a pond when making their dam. This lets multiple other plants and other insects live there and creates a wetland. This also makes it like a giant sponge which helps when there is a drought. In all who wants to kill a beaver?
https://parks.canada.ca/pn-np/mb/riding/nature/animals/mammals/castors-beavers
Some bad things about it would be beavers eat many trees and use a lot of them. Beavers can destroy crops for farmers. People sometimes just find them very annoying.
https://courses.hamilton.edu/beavers/conservation-and-destruction-a-paradox