I suppose it depends whether we want to give more weight to the first use in conversation (1833 or before), or the first use in writing (the 1834 article).
The context of the first use in writing is relevant in either case.
Not to mention the whole crux of this discussion was whether he coined the word for Somerville or not. If he had coined the word in 1833 because Coleridge complained about what they called themselves, then presumably it was unrelated to Somerville.
There is an 1831 letter from Whewell to Somervilles' father, asking him to thank her for the advance copy of her book which she apparently sent him, and also on behalf of the Philosophical Society for the copy she sent them [1] -- so they would have at the very least been aware of her and her book by the time of the 1833 discussion.
It is definitely not clear to me that the assertion in the article is correct, but one thing they do appear to be correct about is that "man of science" appears to have attained substantial currency (or indeed dominance) as an alternative to "natural philosopher" by 1830 [2,3]. Why not keep using that? Perhaps just because it is unwieldy? On the other hand, this was 1830 -- people were not so adverse to verbosity back then.
In any case, the deeper questions of why the profession was thought to need a noun at all, and of Whewell's internal motivations, seem to me still rather unanswered.
Ah I didn't know they corresponded before 1833! That's great to know.
On the other hand
> In any case, the deeper questions of why the profession was thought to need a noun at all, and of Whewell's internal motivations, seem to me still rather unanswered.
I mean Whewell answers this in detail. There's no ambiguity about why the profession was thought to need a noun at all. It's clear they were looking for a single noun, not a string of words. And it's clear that the purpose was an overarching word to promote the unification of the natural sciences. And it's moreover clear it has nothing to do with trying to be inclusive of females at all (I mean Whewell even explicitly uses the word "gentlemen" to refer to these "proto-scientists").
I will re-quote the relevant portion of Whewell's 1834 review (and the only mention of the word "scientist" in the entire review) from elsewhere in this thread.
> And thus science, even mere physical science, loses all traces of unity. A curious illustration of this result may be observed in the want of any name by which we can designate the students of the knowledge of the material world collectively. We are informed that this difficulty was felt very oppressively by the members of the British Association for the Advancement of Science, at their meetings at York, Oxford, and Cambridge, in the last three summers. There was no general term by which these gentlemen could describe themselves with reference to their pursuits. Philosophers was felt to be too wide and too lofty a term, and was very properly forbidden to them by Mr. Coleridge, both in his capacity of philologer and metaphysician; savans was rather assuming, besides being French instead of English;
> some ingenious gentleman [this is Whewell referring to himself] proposed that, by analogy with artist, they might form scientist, and added that there could be no scruple in making free with this termination when we have such words as sciolist, economist, and atheist -- but this was not generally palatable;
> others attempted to translate the term by which the members of similar associations in Germany have described themselves, but it was not found easy to discover an English equivalent for natur-forscher.
It's hard to imagine a more direct exposition in 19th century English of Whewell's internal motivations.
By noun, I mean as opposed to phrase; i.e., unless I'm missing something this does not seem to touch particularly on why "man of science" [/ "men of science"] was not thought to be acceptable, given that it was apparently used about twice as frequently as "natural philosopher" in the surviving books of the time.
I also just noticed that in the 1831 letter, Whewell seems to have been sufficiently impressed by Somerville's book as to write her a poem about it. Such things were presumably more common at the time given that this was the Romantic era, but nonetheless would seem to sugesst that it made an impression on him.
It's pretty clear from all the rejected examples listed they're looking for specifically a one word noun (note they specifically don't mention "natural philosopher" either! Only philosopher). And it's moreover pretty clear that this is a group effort to come up with a word, not just something done by Whewell (he merely contributed the word "scientist").
Given the fact that Whewell uses the word "gentlemen" here, that other people are all doing the same task, and the fact that Whewell outright professes his reasoning for coming up with the word scientist, trying to pin this to Somerville just because the passage happens to be part of a review of her book is really really really stretching it.
As far as I can tell you're relying really really heavily on the coincidence that Whewell has an immense respect for Somerville and the fact that other people happened to use the term "man of science" to argue that he coined "scientist" after Somerville (or at the very least sow doubt in his own stated intentions). And that feels like you're taking Whewell way out of context.
The context of the first use in writing is relevant in either case.