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Consider the following interlocution,
Maria: "A man fell off the cliff!"
Tabish: "He didn't fall, he was pushed."
My professor concluded, This shows that pronouns cannot be the same as the definite description.
Perhaps, she regards Maria's description as referencing 'the man who fell off the cliff', and regards Tabish's reply as expressing that 'the man who fell off the cliff ("He") didn't fall off the cliff', which is a contradiction. But I don't feel confident about that.
A case where a pronoun cannot be substituted by any definite description that may be recovered from the context is discussed by Walter Edelberg in his paper ‘A New Puzzle about Intentional Identity’ (Journal of Philosophical Logic 15 [1986]). Edelberg discusses the sentence in (1) from Peter Geach’s paper ‘Intentional Identity’ (Journal of Philosophy 74 [1967]):
(1) Hob thinks a witch blighted Bob’s mare, and Nob thinks she killed Cob’s sow.
Assume someone utters this sentence to a group of people who are familiar with Hob, Bob, Nob and Cob and their livestock, but who, up until the moment the utterance of (1) is made, have been unaware of Hob’s and Nob’s belief that a witch has been harming farm animals. Assume further that all the participants in the conversation rightly believe that witches don’t exist and that Hob and Nob are wrong. Such a context provides the two definite descriptions in (2) as possible substitutes for the pronoun she in (1):
(2) a. The witch who blighted Bob’s mare
b. The witch whom Hob thinks blighted Bob’s mare
Edelberg shows that there are circumstances in which the sentence in (1) is true, but the sentences derived by substituting (2a) and (2b) for she in (1) are false. He gives the example in (3) (repeated with omissions and slight modifications from his EXAMPLE 2, p. 2):
(3) The Gotham City newspapers have reported that a witch has been on quite a rampage. In reality, there is no such witch. Hob and Nob read the Gotham Star and believe the stories about the witch. Hob thinks the witch blighted Bob’s mare, and Nob thinks the witch killed Cob’s sow. Hob has no beliefs at all about Cob’s sow or about Nob’s beliefs, and Nob has no beliefs at all about Bob’s mare or about Hob’s beliefs.
Under the circumstances in (3), the sentence in (1) is true, but the sentences in (4) are false:
(4) a. Hob thinks a witch blighted Bob’s mare, and Nob thinks the witch who blighted Bob’s mare killed Cob’s sow.
b. Hob thinks a witch blighted Bob’s mare, and Nob thinks the witch whom Hob thinks blighted Bob’s mare killed Cob’s sow.
We can derive from (1) a true sentence if we replace the pronoun she by the definite description the witch reported on in the Gotham Star, but this definite description may not be available to any of the participants in the conversation (perhaps none of them reads the newspapers). The point is that the sentence in (1) may be true even if all the sentences derived from it by replacing she with a contextually available definite description are false.
