I'm curious what makes the "c-word" so much more offensive than other vulgar insults based on female genitalia -- and even more so those based on male genitalia.

I feel like as a non-native speaker I must be missing a significant cultural subtext everybody else seems to be painfully aware of (similar to how someone who's never heard of racial segregation and slavery in the US would be confused why the "n-word" strikes such a nerve).

As far as I know, the difference is intent. Calling someone a cunt is a much greater expression of contempt than calling them a fucker or an asshole. Call someone one of the latter words and there's still a chance it might be affectionate. Call someone a cunt and it removes all doubt.

I get that, but that doesn't seem to be universal at all. There are many communities and regions where "cunt" (or the regional equivalent) doesn't raise any eyebrows.

Why is it that the word is so much more offensive in the US (and England too, apparently) than, say, certain parts of Scotland or Australia?

It's not universal. Cultural definitions count.

It's similar to the word 'fanny'. In the US, it seems it means 'bum'. The word 'fannypack' would translate to 'vagina pack' in the UK, which is pretty funny to hear. The equivalent in the UK is bumbag, where bum is the non-offensive version of arse (which is ass in the US).

Or, for those offended by my slew of filth above, similar to the old chips-crisps problem. American Chips = British Crisps. British Chips = American Fries.

The attacker isn't calling the receiver a vagina. It takes on a different meaning when used like that.

A cunt is loosely defined as a horrible person. To say "he's a proper cunt" is to say "I really don't like him" or "he is deliberately unpleasant".

I find cunt pretty much common among Australians too..