To see a thestral, you need to have seen death. Harry only sees the thestrals in his 5 year, but he also saw his parents die...so why doesn't he see them in his 1 year?
he didn't see his dad die, he and his mum were in the same room together,well he was young after all.
I think it's because he was to young to remember it. In the first book he says he was told that his parents died in a car crash and he believed that because he was only 1. He was 14 or 15 when he saw Cedric die so that's why.