You CAN sign out of the app. But YouTube/Google are sneaky and make it hard to figure out because they want to track everything you do in YouTube and signing out prevents them from doing that.
To sign out from YouTube on iPad
1) Tap your account name in left panel
2) Select 'Use YouTube without a Google Account'' at the bottom of the pop up panel
Note, instead of just calling it a "Sign out" button, not only do they name it something vey dull, but they also go to such an extreme as to change its appearance to not even look like a button. Looks like if you tapped on it you would be reading some instructions or a boring EULA text. So basically, it's a deliberate attempt to subvert their users' efforts to simply log out by making you confused and frustrated enough to either give up and let them continue tracking every video you watch, or to make you resort to the Internet for answers on pages like this. Google sucks. So much for their "Do No Evil" motto. This kind of obfuscation is pure evil stuff.
Is it even more insidious on a laptop, every time I gmail and forget to sign off, am permanently identified by Google it tracks what I am doing, send those information to vendors and in short order am being spam. Evil.