Why does iTunes think that it is quitting "unexpectedly" every time I quit?

Solution 1:

The EtreCheck scan has found multiple pieces of adware on your Mac, remove them all. My guess is that one of these adware were trying to hook into the iTunes executable (or the operating system itself) and causing the crashes when iTunes was trying to terminate.

You can find instructions on how to remove Conduit here. I'd remove this first and then open the Extensions window in Safari and uninstall the three extensions that were identified as adware.

You have Sophos installed. I'd make sure it is up to date and updating regularly. Ideally you'd have hoped it would have caught and prevented these infections.

In the interests of system stability, I'd also go through the list of installed software that EtreCheck has found and remove anything you no longer use. For example the Startup Items which no longer work in Yosemite.