Because you can’t. Sorry, I know that may seem like a harsh way to start, but I figured it might help to have clarity from the start.
The reason you need to link an Azure subscription to a Visual Studio Online (VSO) account is so that VSO can use your Azure account’s billing mechanism to bill for additional VSO users, build minutes, or virtual user minutes that you need beyond the free users and minutes. So you can only do that with a paid Azure Subscription that has an active billing configuration.
I speak for myself here, I’m not part of the group responsible for this, but my speculation as to why you can’t do it is as follows. If you were allowed to link your MSDN Azure subscription though, there is a built in credit in that subscription. You would effectively be able to use your free MSDN Azure benefit to provide paid VSO access to others. That just doesn’t make sense, using your benefit to give access to others. So for now at least, it just isn’t allowed.
If you want to play with Visual Studio Online paid accounts or minutes, you could create a Free Windows Azure Trial subscription, and link it to a Visual Studio Online account. You might consider creating a special Microsoft Account (a.k.a. Live ID) just for the test, and create the test VSO and Azure subscriptions using that test Microsoft Account.
Note, if you do go to create a new Microsoft Account for the test, it helps to do that in an “InPrivate Browsing” (Ctrl+Shift+P in Internet Explorer) or an “Incognito Window” (Ctrl+Shift+N in Chrome) window so you don’t conflict with your regular Microsoft Account.