Learn English – What’s the origin of the idiom “miss the boat”

There's a related discussion over at The Phrase Finder:

I think it comes from a time (not long ago) when everyone wore hats, and many of those hats were specific to a given trade, official position or function. So someone who had several roles would have several hats and would wear the appropriate one for the occasion. [...] "which hat will you be wearing?" would mean "in which capacity will you be attending?"

As you can see, it's just speculation without citing any sources, so I have looked it up in the American Heritage Dictionary of Idioms, and here's what it has to say:

wear another hat Also, wear a different hat or two hats; wear more than one hat. Function in a different or more than one capacity or position, as in I'm wearing another hat today; yesterday I was a housewife, today I'm an attorney, or I wear two hats—are you asking me as a member of the city council or as a storeowner? This metaphoric expression alludes to headgear worn for different occupations. [Mid-1900s]

So it's indeed a metaphor, and a relatively young one.

"Enough is as good as a feast"