Objective of UnitTesting is simple - reduce cost of writing and supporting of an application. It's a very high level one. For developer there are few others like: writing better code, saving time on debugging, easier maintain, professional growth after all.
UnitTesting is completely developers job, and yes you will need to maintain addional project with tests, but it worth this effort. (this will not be a copy of your project btw)
Unit Testing is fun. It just fun to write and run tests. You won't understand until you try.
Unit Testing is whole different way of writing code and working with code base. You should understand this and all youyour team members too. You will need to run tests often, setup CI, feel happy.
Unit Testing is have a good tooling and a big community around, so starting writing tets will not be very hard.
When you have Unit Tests you can't say that project is shining and everything is great, but when after that you get involved into project without tests you starting to understand all importance of them.