Because Signing In is now a requirement. When you Sign Out that is how you Deactivate the install on that computer so you can move the install to another computer.
So once you Sign Out when you Sign back In, whether on that same computer or a different one, you have to then re-enter the serial number.
So if you are not moving LR from one computer to another don't Sign Out. Nothing happens if you stay signed in.
OK, so "sign out" means "deactivate". Is there a Help\Deactivate that will sign me out? Why would I want to be connected to Adobe all the time I'm using LR? If nothing happens if I stay signed in, why are we wasting the bandwidth and opening our machines to anything coming through from Adobe? Why not sign out since nothing is happening? Must be some reason they are having us signed in and not allowing us to sign out. And this wasn't in the package I bought over a year ago.
You are not connected to Adobe all the time. Signing In is a prerequisite to use all of the new Adobe apps. If you don't want to do that or you want to continuously sign out then be ready to enter your serial number every time you use LR (along with Signing Back In).
Once Signed In you can disconnect your computer from the internet and LR will still function with every option available.
Or switch to some other image editing program.