CIRP.org has this interesting article from 1867 Medical Times and Gazette. This was the article that ended the career of Isaac Baker Brown, infamous FGM practitioner of the time, who used clitorectomy to cure all sorts of "diseases" in women, including hysteria, excessive libido, lust, itching and so on. Baker Brown basically considered both FGM and circumcision to be parallel operations with similar aims (prevention of various diseases and reduction of libido), and he justified FGM the same way as circumcision used to be justified by the practitioners of the time.

Here's the article.

http://www.cirp.org/library/history/medicaltimes1867/

The opinions expressed are roughly similar to the mainstream thought of today, article claims that FGM is incomparable to circumcision, condemns Baker Brown for carrying out FGM, and so on. But, there is one surprising passage:

It is a second error to assume that if a woman desired to continue filthy habits this operation would stop her. The organ removed is but one amongst many susceptible of intense excitement.

The article says that FGM is bad because, among other things, women will still have lustful thoughts. FGM is bad because it doesn't eliminate dirty thoughts and urges in women!

For Victorians, excessive sexual desire was an embarrassment and something to be curbed by any humane means. This is why they promoted male circumcision and why Baker Brown used to perform FGM for a while.

But, this article condemns FGM because it (allegedly) does not eliminate excessive sexual desire. Baker Brown did not manage to convince them that FGM dampens female sexual desire, and thus FGM was declared to be a useless (and potentially dangerous) operation. FGM and Baker Brown were condemned, FGM was no longer practiced in UK and Baker Brown was forced to abandon his practice.

This is entirely different from our modern thinking. For us, anything that curbs sexual desire is bad, and we condemn FGM because we believe that it does so (but not male circumcision). For Victorians, anything that curbed sexual desire was good, and they condemned FGM because they believed that it did not.

It is interesting that Victorians believed pretty much what we do today, (FGM bad, MGM good), but they justified their beliefs by a different logic, completely opposite logic, in fact.