Why do I have to allow or deny iTunes or any other software, access to the internet?

Did you install Little Snitch (or Hands Off)? It will post a dialog to allow/deny apps calling out if you don't allow it to record what it is to permanently do if it sees the same call again from the same app.

Little Snitch will post a dialog with allow/deny buttons. But there is also three tab buttons; once, until quit, forever. "Until quit" is the default. So it won't nag about the same call again until that app quits but it will if you relaunch that app and the app makes the same call out. Choose "once" will allow that one call to be placed but will cause LS to nag the next time that app tries to call even if you haven't quit. Choose Forever and it will never nag again about that specific all attempt.

You need to train LS which apps you want to permit calling out and which ones you never want to allow calling out. You will of course initially be nagged quite often as you are seeing. But if you train LS to always allow the ones you want to allow eventually there will be fewer and fewer dialogs since your habits don't change that radically in the way you use your own machine.

Can you post a picture of the dialog?