Why does Logan Airport's Runway 32/14 only have arrivals on the 32 heading?
(Much of my answer below will be drawn from "The 30-year saga of 14/32", a 2006 Boston Globe article which is unfortunately subscription-only but which I have access to via an institutional database.)

Runway 14/32 has been a long-standing bone of contention at Boston Logan.  Like many urban airports, Boston Logan is constrained by the fact that there are many people living nearby who don't particularly like jets flying low over their houses, and who are willing to organize in opposition of any increase in operations at the airport.   Massport, the organization in charge of Boston Logan, had originally proposed to build a new runway in the late '60s.  This met fierce opposition from community members in East Boston who were opposed to additional take-offs and landings over their homes.


  [I]t's taken no less than 33 years for 14/32 to become reality, a testament to how politically charged Logan expansion has been ever since demonstrations in the 1960s, when East Boston mothers lay in the streets to protest the destruction of Eastie parks and homes.  ...


The Hyatt Harborside Hotel (now the Hyatt Regency Boston Harbor) was built in the 90s to act as an impediment to runway expansion:


  In the 1990s ... Frederick P. Salvucci engineered construction of the 270-room Hyatt Harborside Hotel, a stone's throw from the end of the new runway, largely to create as big an obstacle as possible to Massport extending 14/32 or using it for planes flying over the city.


In the end, Boston Logan was barred by court order from allowing takeoffs from 32 or landings on 14, except in emergency:


  By court order, use of 14/32 will be restricted to planes taking off and landing over Boston Harbor, so Massport will be legally forbidden - except in emergencies - from using the runway to let planes take off or land over South Boston and downtown.


This still allows for three runways to be operative when winds are from the northwest or southeast (along with 15L/R or 33L/R), so the hope was that even this "half-runway" would result in fewer delays at BOS during bad weather.  Whether or not this has panned out to be true in the decade since, I do not know.