Not only did Jeremy hate his family. He hated Crispy to.
Crispy and Jeremy didn't get on I believe, Crispy used to bite Jeremy, he was by this time very old and may have been kept alive too long as some dogs are.
If Jeremy had killed 5 people in the farmhouse and he hated Crispy, surely he would have shot the hated little dog, if he was able to murder 5 people the way it's said he did then he would surely have killed Crispy without a second thought?
Think AE had him put down as she didn't want him either. Poor old Crispy was probably totally and irretreveably traumatised, it was possably the only option.