The "douche" part is easy. Anything associated with the crotchal region, however tangentially, eventually makes its way into the lexicon as an insult. These terms are insults because they carry a connotation of being "dirty," physically and/or morally. However, I think that most people would agree that calling someone a douchebag is a step up in the degree of insult, and that is what is curious. If we naively try to interpret its meaning based on what a douchebag actually is, it should be, if anything, a milder insult, if not a complement, as it is an implement with the specific function of remedying the very dirtiness that is the basis of any crotch-related insult.
Obviously, that is not the right way to parse "douchebag." When we call someone a douchebag, we are really calling them a douche + bag. It works through analogy to the other "-bag" insults, like dirtbag or scumbag. Suffixes like "-bag," "-sack," and "-bucket" function as as intensifiers, or perhaps insultifiers. They can be productively added to just about anything, and it sounds more insulting. "Jerkbag" sounds worse than "jerk." In many contexts (e.g., volleyball), calling someone a "wall" might be a complement. Calling someone a "wallsack" would be mostly confusing, but could probably safely be interpreted as an insult.
I think that these modifiers implicitly deny the emergent humanity of the insultee, by reducing them to no more than the sum of their constituent parts. Stick with me here. The fact is, the very thing that makes us human -- or alive for that matter -- is not the components that make us up, but rather the complex relationships among those components. To quote Patty Loveless, "Break us down / to our elements, / and you might think He failed. / We're not copper for / one penny or / even iron for one nail." [1] The critical attribute of a bag or a sack is that its contents are disordered, and that complex functional or structural relationships among those contents are unlikely to exist. If someone calls you a douchebag, they are both calling you a douche and implying that your value is not greater than the sum of your parts.
What I like is that the productive family of suffixes "-bag," "-sack," etc. implies a sophisticated, if unconscious, understanding that the essence of our humanity is a classic emergent property, not derivable from a simple summation of our human components. For those of you who aspire to greater explicitness when insulting people (I know you're out there), let me suggest the following variant next time you are thinking of calling someone a scumbucket: "high-entropy scum."
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[1] This is not technically true anymore, since the introduction of copper-plated zinc pennies in 1982. According to Wikipedia, penny weighs about 2.5 grams, and is now about 2.5% copper, which means that it takes about 62 mg of copper to make a penny. According to the Copper Development Association, the human body contains perhaps 100-200 mg of copper, depending on the size of the particular human body in question. So, we are, in fact, copper for one penny, but most of us are not copper for four pennies. In Patty's defense, the song was released in 1994, and, given that coins can commonly last for 25 years or more, the majority of the pennies in circulation at the time may well have been of the pre-1982 variety, containing 15 to 20 people worth of copper.