Native or custom look and feel for desktop applications

I am currently writing a library to create desktop user interfaces, and I am asking myself a question: is it better to have a native look and feel, or a consistent custom look and feel?

I personnally think that, today, custom look and feel is important because it gives a real identity to the application, and it helps to highlight features. Moreover, every professionnal application uses custom look and feel, from what I saw. However, I talked with someone and he pointed the fact that a consistent design whole the system can be important in term of user experience. So, I was wondering if I really need to support native operating system components.

Just to clarify, by "native components", I mean the normal design of buttons, text fields, dropdowns, menus... For example, on windows, these things look like this:

Thank you for your help!