In Beyond Freedom and Dignity Skinner writes (page 21)

A more important reason is that the inner man seems at times to be directly observed. We must infer the jubilance of a falling body, but can we not feel our own jubilance? We do, indeed, feel things inside our own skin, but we do not feel the things which have been invented to explain behaviour. The possessed man does not feel the possessing demon and may even deny that one exists. The juvenile delinquent does not feel his disturbed personality. The intelligent man does not feel his intelligence or the introvert his introversion. (In fact, these dimensions of mind or character are said to be observable only through complex statistical procedures.) The speaker does not feel the grammatical rules he is said to apply in composing sentences, and men spoke grammatically for thousands of years before anyone knew there were rules. The respondent to a questionnaire does not feel the attitudes or opinions which lead him to check items in particular ways. We do feel certain states of our bodies associated with behaviour, but as Freud pointed out we behave in the same way when we do not feel them; they are by-products and not to be mistaken for causes.

Dennett writes (page 83)

The heterophenomenologlcal method neither challenges nor accepts as entirely true the assertions of subjects, but rather maintains a constructive and sympathetic neutrality, in the hopes of compiling a definitive description of the world according to the subjects.

So far Skinner and Dennett are not disagreeing. Skinner did say "We do, indeed, feel things inside our own skin,...". He can hardly object to Dennett writing down our descriptions of what we feel, as verbal behaviour to be explained in the future with a reductionist explanation.

Dennett continues on page 85

My suggest, then, is that if we were to find real goings-on in people's brains that had enough of the "defining" properties of the items that populate their heterophenomenological worlds, we could reasonably propose that we had discovered what they were really talking about --- even if they initially resisted the identifications. And if we discovered that the real goings-on bore only a minor resemblance to the heterophenomenological items, we could reasonably declare that people were just mistaken in the beliefs they expressed.

Dennett takes great pains to be clear. I feel confident that I understand what he is taking 500 pages to say. Skinner writes more briefly, 200 pages, and leaves room for interpretation. He says that we do not feel the things that have been invented to explain behaviour and he dismisses them.

I think it is unambiguous that he is expelling the explanatory mental states of the psychology of his day (such as introversion) from the heterophenomenological world of his subjects, on the grounds that they are not things that we feel or talk about feeling. But he is not, in Dennett's phrase "feigning anesthesia" (page 40). Skinner is making a distinction, yes we may feel jubilant, no we do not feel a disturbed personality.

What is not so clear is the scope of Skinner's dismissal of say introversion. Dennett raises the possibility of discovering meaningful mental states that actually exist. One interpretation of Skinner is that he denies this possibility as a matter of principle. My interpretation of Skinner is that he is picking a different quarrel. His complaint is that psychologists claim to have discovered meaningful mental states already, but haven't actually reached the starting gate; they haven't studied enough behaviour to even try to infer the mental states that lie behind behaviour. He rejects explanatory concepts such as attitudes because he thinks that the work needed to justify the existence of such explanatory concepts hasn't been done.

I think that the controversy arises from the vehemence with which Skinner rejects mental states. He dismisses them out-of-hand. One interpretation is that Skinner rejects them so completely because he thinks the work cannot be done; it is basically a rejection in principle. My interpretation is that Skinner rejects them so completely because he has his own road map for research in psychology.

First pay lots of attention to behaviour. And then lots more attention to behaviour, because it has been badly neglected. Find some empirical laws. For example, One can measure extinction times: how long does the rat continue pressing the lever after the rewards have stopped. One can play with reward schedules. One pellet every time versus a 50:50 chance of two pellets. One discovers that extinction times are long with uncertain rewards. One could play for decades exploring this stuff and end up with quantitative "laws" for the explanatory concepts to explain. Which is when serious work, inferring the existence of explanatory concepts can begin.

I see Skinner vehemently rejecting the explanatory concepts of the psychology of his day because he thinks that the necessary work hasn't even begun, and cannot yet be started because the foundations are not in place. Consequently he doesn't feel the need to spend any time considering whether it has been brought to a successful conclusion (which he doesn't expect to see in his life-time).