Why are human children more likely to get lice (nits) than adults?
Children generally don't care about their hair as much as adults do. So unless parents insist, they don't care for their hair as much (reference). Kids generally get lice because they are in close contact with each other during play-dates, slumber parties, and sports activities. They are also prone to exchange hair brushes and other personal items more often than adults (reference). 

An interesting difference I came across between articles is that one article says that its


  theoretically possible to get infested if your hair makes contact with
  items such as hats, combs, or brushes (reference).


Another article insists that 


  You’re extremely unlikely to get head lice by sharing hats, combs or
  pillows – a louse’s lifespan is very short once it’s removed from your
  head (reference).


Between the two, I believe that it is extremely likely that lice would spread if you use a infected hairbrush immediately after it was used by someone harboring the parasite since the time span is short.