What is the etymology of the term "perverse sheaf"? Grothendieck famously objected to the term "perverse sheaf" in Récoltes et Semailles, writing "What an idea to give such a name to a mathematical thing!  Or to any other thing or living being, except in sternness towards a person—for it is evident that of all the ‘things’ in the universe, we humans are the only ones to whom this term could ever apply.”  (Link here, in an excellent article "Comme Appelé du Néant:  The life of Alexandre Grothendieck", part 2, by Allyn Jackon.)  But a google search for '"perverse sheaf" etymology' gives only nine hits, none of which seem informative.

What is the etymology of the term "perverse sheaf"?

 A: "Goresky and MacPherson relaxed the transversality condition
on the cycles by allowing them to deviate from dimensional transversality
to each stratum of codimension k, for each k > 2 (by
hypothesis there are no strata of codimension 1), within a tolerance
specified by a function p(k), which they called the perversity." From the book review Link of Kirwan's book on intersection homology.
A: The word "perverse" has strong and jarring connotations in some languages, such as German, but became standard usage nonetheless.
One of the founders of the theory said that the term was unpopular with everybody except for one specific mathematician --- who was another of the famous founders.
A: When MacPherson and I first started thinking about intersection homology, we realized that there was a number that measured the "badness" of a cycle with respect to a stratum.  This number had the property that when you (transversally) intersected two cycles, their 
"badness" would add. The best situation occurs for cocycles, in which case that number was zero, and the intersection of two cocycles was again a cocycle.  The worst situation was for ordinary homology, in which case that number could be as large as the codimension of the stratum.  In that case, the intersection of two cycles could even fail to be a cycle.  After a while it became clear that we needed a name for this number and we tried "degeneracy", "gap", etc., but nothing seemed to fit.  It seemed that the bad cycles were being "obstinate", but "obstinateness" did not sound reasonable.  Finally we said, "let's just call it the perversity, and we'll find a better word later". We tried again later, with no success.  (We did not realize that in some languages the word is obscene.)  When we first went to talk with Dennis Sullivan and John Morgan about these ideas, we were calling the resulting groups "perverse homology", but Sullivan suggested the alternative, "intersection homology", which seemed fine with us. This was 1974-75.  Later, when it was discovered that, for any perversity, there is an abelian category of sheaves, whose simple objects are the intersection cohomology sheaves (with that perversity) of closures of strata, Deligne coined the term "faisceaux pervers".
A: When I was a grad student, a classmate commented about the odd term "perverse" in IH but I defended it. I thought I had figured out the rationale, which I denied had anything to do with perversity in the ordinary sense of that word. My theory was that the "verse" was from "transverse," which is a generic kind of intersection of objects of complementary dimension. By replacing "trans" with "per" we get a more general notion of intersection. The "per" here meant excess or abundance, following the way chemists use that prefix in words like peroxide or permanganate. A perversity in IH in fact specifies how far in excess of the generic expectation the dimension of an intersection with a stratum is allowed to be. My classmate was skeptical, but this theory seemed so plausible to me that I never really doubted it. I am genuinely surprised to be finally refuted.
A: One explanation I heard (it may have been from MacPherson but I am not sure) was that "perverse" was used in the sense of "contrary", the cycles used in the definition refuse to move away from the singularities.
A: Here's what I like to think, me and my ignorant self.  Why name something after a word?  Most folks would do it because they think that whatever meanings and connotations that word already carries would apply well to the concept being named.  I see your quoted Grothendieck as a strict practitioner, and indeed a master, of this style of naming: think of "etale", "crystalline", "topos"...
However, this point of view ignores an important aspect of the naming process -- its bidirectionality.  Once you name something after a word, the word is forevermore changed in its meanings, connotations, usage, and cultural presence, by simple virtue of being attached to this thing it wasn't attached to before.  That is, it's possible to view the act of naming not as applying a word to an object, but applying an object to a word.
Coming to perverse sheaves, the question was why such "beautiful" and "well-behaved" objects deserved the name perverse.  Certainly from Grothendieck's perspective on naming this seems to be a travesty; but from the second perspective it makes perfect sense: how better to soften the harsh and pejorative word "perverse", at least in certain (mathematical) circles, than to apply it to such fantastic objects?
I view the naming of perverse sheaves as a brilliant and subversive act.
