That's actually the exact opposite of where you'd want to be in a northern hemisphere cyclone.
In general, the "right hand" (east half) of one of these storms will have more severe conditions, mostly due to the movement of the storm itself adding to the intensity of conditions on the surface. This is what the "dangerous semi-circle" term comes from. Not every storm is perfectly symmetrical and interaction with other pressure systems (particularly highs in the vicinity) can affect this.
That being said, Joaquin pretty much planted itself over The Bahamas on Thursday and Friday with little movement. This was in contrast to the forecast which had it headed north-ish at a much faster pace. Without assuming too much, it's possible that the captain was counting on it being well to the north of them by the time they got there, which would also start putting the winds and seas on the quarter.
A historical track of all hurricanes in that area is posted here:
http://www.wunderground.com/hurricane/atlantic/2015/tropical-storm-Joaquin?map=historical
Joaquin stands out as the the only one that hooked very slowly to the SW, nearly stalling, then finally heading NE. It's a very distinct track as compared to the others.
Running south of The Bahamas and taking Old Bahama Channel might look good in hindsight but it locks you in between Cuba and the islands while in relatively shallow water. No place to run if you do that.
Unless local prevailing conditions/hazards exist which prevent otherwise, ships like this on short liner runs almost always put to sea on schedule no matter what. They'll divert if they have to, but staying in port is something just not done for many reasons. As has already been pointed out, had Joaquin headed towards FL, Jacksonville (St Johns river) is one of the last places you'd want to be stuck in with a ship like that.
This was a very experienced and well-educated Master. It's too much of an easy cop-out to say that he was an idiot and unless anybody else here has ever had that burden of responsibility placed on their shoulders (AFAIK, deepdraft1 is the only one here who can legitimately claim that), then you can't understand all the factors that he had to balance before making a decision.
As Beyond said, this isn't black and white. The people crying "they shouldn't have gone" are generally the ones with zero real seagoing experience.