In the "Chamber of Secrets" Harry can't see the thestrals because he did not actually see the death of his mother. He was a newborn baby and his mother was covering his body to protect him. She was struck by Voldemort and killed then Voldemort tried to kill Harry but he was not killed. He received the "Z" shaped scar on his forehead as a result of the attack by Voldemort. He does not see them until "Harry Potter and The Order of The Phoenix." This is following "Harry Potter and the Goblet of Fire," which is the book that Harry sees Cedric die.
The ability to see the thestrals occurs only after one actually witnesses the death of another person. It is the same idea as the petrification of the people who saw the basilisk. Anyone who saw the basilisk was suppose to die immediately, however, the cat saw it's reflection in water, Colin saw it through a camera, and Hermonie saw it through a mirror. So no one actually looked right at the basilisk. J.K. Rowling is a master at "spitting hairs" in her stories. Even though Harry was present when his mom died, he did not actually "witness her death, so he couldn't see the thestrals until after he had seen Cedric die.
“Lily, take Harry and go! It’s Him! Go! Run! I’ll hold him off-”.
The sound of someone stumbling from a room-a door bursting open - a cackle of high-pitched laughter.
“Not Harry! Not Harry! Please not Harry!”.
“Stand aside, you silly girl ... stand aside, now . .
“Not Harry, please no, take me, kill me instead-Not Harry! Please ... have mercy ... have mercy”. (Rowling, 1999, pp. 134 and 178).
Hope this helps.