As far as I can tell after reading that review captured in the archive.org link, Bergland's quote in the brainpickings.org article is inaccurate.

1. Whewell did not coin the term "scientist" (an unnamed "ingenious gentleman" did, unless Whewell slyly intends this to refer to himself, which seems unlikely since he remarks "this was not generally palatable") EDIT: It seems Whewell probably did coin the word "scientist" and this was indeed a sly self-reference.

2. "Scientist" was not coined for Somerville, but instead likely predates Somerville's On the Connexion of the Physical Sciences. Whewell seems to suggest the term arose during one of the meetings of the British Association for the Advancement of Sciences "in the last three summers" (i.e. 1-3 years before the publication of Somerville's book).

3. Whewell, at least in this article, never refers to any single person as a "scientist" and in particular does not call Somerville a scientist.

4. "Scientist" was not coined for reasons of gender, but for unifying investigators of the various subdisciplines of the natural sciences under a single name.

The only thing I can tell that is true is that Whewell speaks very highly of Somerville and is clearly an admirer of her work, especially because Somerville is a woman, and so Whewell is certainly taking Somerville's gender into account in his overall review.

This it the full text of the relevant quote (and the only time the word "scientist" shows up in the review as far as I can tell), with the direct sentence broken out.

> 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, beseides being French instead of English;

> some ingenious gentlman 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 palatble;

> 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.

EDIT: Apparently @ska has found the same thing.

EDIT 2: Looks like I was wrong about Whewell not coining "scientist." @disown refers to Snyder's TED talk where she mentions that Whewell did in fact coin the word "scientist" in response to Coleridge at the 1833 meeting of the British Association for the Advancement of Science.

Snyder's book The Philosophical Breakfast Club makes reference to this event, but I cannot find the original source. A report on the 1833 meeting (https://archive.org/details/reportofthirdmee34lond) does not contain mention of this event. Perhaps someone else can track down the original account?