I have also identified my computer security software (McAfee) as the reason behind encountering this issue. My solution was to disable both the ant-virus and firewall protection when installing the update to the newest version of iTunes; in this case version 12.2.2.25. Furthermore, I suggest after installation you ensure you are able to sign-in successfully to your iTunes account (with your Apple ID) as well as open and close the iTunes software a few times to ensure successful loading before re-enabling any security software. At this point, I am able to keep McAfee as my software solution without having to revert to using Windows Defender; as "TCP1 P" mentioned above this post.
My best guess is that it is actually on McAfee's end or whatever other security solution you may have if the fix actions work the same for you. I say this because if the newest update to iTunes hasn't actually made it onto McAfee's "whitelist" to declare it as a known good file/application, it will trigger as bad and may prevent whatever last installation/registration measures (be it on the host or accessing the network/internet) that Apple requires of any newly installed instance of the iTunes client. I am reviewing my McAfee logs to note whether this is the case or not but since it is taking forever I will post this here in the effort to help anyone who is having the same issue. I will say I do question what new changes Apple has made to this latest update that now triggers a response from my security software but again, I will have to look into that later if I choose to do so at all.