'The English instinctively admire any man who has no talent and is modest about it,' said the critic James Agate.
(He was actually James Evershed Agate, but he didn't like to draw attention to his classy middle name.)
On the whole the English don't like loud or boastful people. It's thought more seemly to refrain from mentioning successes and acts of heroism.
(I'd give you an example from my own experience, but that would be, well, brash.)
This makes life rather difficult in an age of social media. If nagged enough by a publisher I might possibly start a blog...well, I might as long as it didn't involve mentioning my, um, books too often, anyway.
Brash does have a couple of other meanings: it can mean loose rubbish (hedge-clippings or rocks), or it can mean heart-burn type indigestion.
So, come to think about it, all brash's meanings are pretty much the same thing, aren't they.
Thing Not To Do Today: be brash. The boasting word might come from rash, which comes from the Old High German rasc, hurried or clever, and is related to the Old Norse roskr, which means brave.
No one knows where the other meanings come from, though my Collins dictionary suggest the heart-burn brash might be of imitative origin.
Of what it might be imitative, I really have not the faintest idea.