The basic reasons of using MVVM are Separation of Concerns (SOC) and Single Responsibility Principle (SRP). Then you have Flexibility, Maintenance and Testing.
The goal of MVVM was to apply the above on WPF. WPF provides "plumbing" to allow easy use of MVVM through Data Binding.
For SOC and SRP read: Separation of Concerns(Wikipedia) and Single Responsibility Principle(Wikipedia). But the basis is: The logic doesn't care that the button is red and situated on the left top corner. Only the UI cares about it.
Flexibility on this case is the ability that one ViewModel can provide to different Views, or one View can use several ViewModels, that one ViewModel can use more that one Model, and that a Model can be used on separate ViewModels.
Maintenance is a consequence of SOC and SRP. It is much easier to change parts of the code or UI without affecting other sections.
For Testing, now you can do automated testing of your logic without having a window pop up. You can isolate the tests and mock whatever is needed (if at all).
To the product owner what you have to say is that it will become easier to make changes and to affirm(test) that the application is behaving as expected.
To the developers: it will make your life easier.
If you are not using WPF, maybe look into MVC(Wikipedia) or MVP(Wikipedia)