Deleted apps on my iPhone stays in iTunes When I delete an app inside iTunes from the iTunes Library, it will also get deleted from my iPhone, the next time I sync. The same with if I download a new app, it will be transfered to the iPhone.

When I install an app on my iPhone it will also be imported to the iTune library, however when I delete an app on my iPhone, it doesn't get deleted from iTunes automatically?

Why? And how can I change this?
Allow me to answer this by providing a counter-example.

I own two iOS devices; An iPhone 4 and an iPad (original). I use slightly different application sets on them. For example I don't have a notification app called Prowl on my iPad because it's intended use is to get my attention anywhere I am. And the iPhone is always by my side or at least in very close proximity.

And of course, there are iPad only apps such as the iWork series until recently. Even then, I only have the iWork apps on my iPad because working on something like that on an iPhone is admittedly kind of terrible.

So, when managing my apps, if deleting an app on device deleted it in iTunes, the other device would lose the app on next sync. This is not a good thing for me.

When you delete an app in iTunes, it unchecks it from the sync list. This way you continue to receive updates for it via iTunes, and if you ever want the app back, it's a simple operation to check the box.

I do believe @Hand-E-Food's example of a paid app is a good example. While we know that you can re-download any app not in your library you already paid for, not having to jump through the "Yes I do want to re-download this app I purchased" hoops is handy.

If you deleted an app because of crashes or general instability, than you can watch iTunes and wait for it to update, and then update it and see if it's better.

Why is best answered by Apple themselves, as it was obviously a design consideration that I'm not sure anyone else here will have the answer too.

But unfortunately I don't believe you can change it. The easiest way to change it would be to delete apps only via iTunes, and not on your iPhone directly.