Of course there is. So forget about that argument right away. We cannot observe the mind. This means that as our theory scales up to explain more and more of the things our minds can DO, we can only hope that somehow that will capture what we FEEL too, because no one has any idea how to reverse-engineer feelings, as opposed to doings. And in my opinion, no one ever will.
Feelings exist, that's undeniable.
I know what it feels like to be typing right now, but you have to take my word for it, because you aren't me, so you can't feel my feelings. You have a pretty good idea of what it feels like, because you have had similar feelings too. But there is no way to make a science out of those feelings. I think what you meant was that Watson rejected theorising about the mind because the mind is not objectively observable, whereas behaviour is. Psychologists finally realised that there's nothing wrong with theorising about unobservables, as long as the theory is testable against observable data.