OP, I don't think you're being unreasonsable to think that, but personally it's a word I wouldn't use except in company of those I knew well, and never in front of kids. (That said, I don't say 'fart' infront of children).
Thought this was an interesting debate. I remember being told by an English teacher that the word originated in very Early English and that the equivalent (which I cannot remember) was not supposed to be obscene in Chaucer's time.
Language is always changing. Expletives generally come in and out of fashion & degrees of 'taboo' - 'by our lady' became 'bloody' which was considered offensive 100 years ago and is now pretty harmless. Geography also plays its part - 'pissed' in the States means 'bored' or 'fed up' and I don't think (but may be wrong) is as rude as being 'pissed off' in British English.
WRT the whole thing of why a slang word for female genitalia is deemed more obscene than any of the many terms for the male parts is down to misogyny I think. I can understand the whole argument for 'reclaiming' the word, but haven't got the balls [so to speak!] to discuss my c... in Starbucks. 
Just out of interest, I looked up the origins of the C word (online):
definition on Dictionary.com
"female intercrural foramen," or, as some 18c. writers refer to it, "the monosyllable," M.E. cunte "female genitalia," akin to O.N. kunta, from P.Gmc. kunton, of uncertain origin. Some suggest a link with L. cuneus "wedge," others to PIE base geu- "hollow place," still others to PIE gwen-, root of queen and Gk. gyne "woman." The form is similar to L. cunnus "female pudenda" (also, vulgarly, "a woman"), which is likewise of disputed origin, perhaps lit. "gash, slit," from PIE sker- "to cut," or lit. "sheath," from PIE kut-no-, from base (s)keu- "to conceal, hide." First known reference in English is said to be c.1230 Oxford or London street name Gropecuntlane, presumably a haunt of prostitutes. Avoided in public speech since 15c.; considered obscene since 17c.