iTunes Won't Quit

Just this once (right click on the application in the Dock and there may be a force quit selection there), or is this something which repeatedly happens? If repeatedly, try starting iTunes while holding down the option/alt key and create a test library. Will iTunes quit from this? If it will then there is some characteristic to your old library or the services it invokes which are holding up things. What I mean by "services" is iTunes is trying to do a ridiculous number of things these days and it is probably designed thinking everybody has modest libraries and high-speed Internet connections with nothing being slow on the network or the servers at Apple's end (dream on).

Well, maybe Linc Davis will check this topic and post a detailed set of instructions on how to trouble shoot specific components of iTunes. Generally though you are limited at actually doing something about those components unless it is something that went wrong at the installation stage (re-install the application), or you are prepared to disable a feature of the application. Since iTunes seems to work fine with an alternate library it is unlikely to be a corrupt application. You will have to provide a lot more details on your system configuration, your iTunes library (are we talking 500,000 tracks here?), and what other features you are running such as Apple Music, Match, Genius? Either that or you can work under the assumption that since another library seems to not present problems it is the library file itself which is corrupt and go about restoring it (iTunes Library.itl) from a backup, or from an old version, or even rebuild your library from its related .xml file or even from scratch.