Because it's like they're saying that there is a singular "British" accent... There isn't a singular British accent. There are many, many very different accents sometimes varying from town to town within counties.
I have a BRITISH accent, as I am from Great Britain, but my accent is a mixture of Liverpool, Cheshire and Welsh as I am from the Wirral. I sound VERY different from someone from "the south" and even to someone from Manchester or Leeds, or Bolton, or Oxford, or London ( I could go on) - totally different pronunciation and even rhythm in how we talk.
The accent that is generally considered "British" is more akin to received pronunciation or "Standard Southern English"
I'm KNOW that within America there are more than Just "New York" and American accents as someone from Alabama is going to have a TOTALLY different accent to someone from Virginia, or Boston, or California. I was using "New York" as an example of how you shouldn't just say that one dialect is seperate from an entire country of different accents and dialects under one "umbrella"
Sorry, it just annoys me when someone says "I can do a British accent" and starts spouting in some kind of Dick Van Dyke-esque cockney accent. If they the OP had said a "generic" British accent then I would have not been as annoyed.
I hope I've explained myself a little bit more as it just bugs me when people think everyone from GB talks like Harry Potter, the Queen or Bert!!