First, you have the absolute most control you will ever have over your application. This may not be true when a particular tool becomes popular, say at the release of a new tool, but this definitely shows up as time progresses. Who knows what tools will keep up with the native frameworks terms of functionality?
Another reason that is more qualitative, is that you come into contact different design styles, code styles and paradigms. Objective-C, for instance, is a tricky beast sometimes, but it is an interesting language with a lot to learn both good and bad. The new things you learn will most definitely carry over into your web programming!
The third reason to code natively, and I cannot stress this enough, is third-party library support. Maven and cocoa pods may dependency management much better on the mobile platforms, and using a third-party tool will most likely render all those advancements useless. There are some amazing libraries for both platforms that you definitely don't want to miss. They were reduce the amount of time you spend coding and improve your baseline quality.