Similarly to Dobby, Hedwig's death is horrible because of her innocence. She [was] Harry's sole companion on all those summers away from Hogwarts, and [was] by his side as a reminder of the wonderful turn his life took when he turned 11. She was a source of security and comfort, both at Hogwarts and when [he was] stuck back on Privet Drive. I didn't know at the time that her [death] was basically a practice run for the reaction I'd have when innocent, loyal Dobby was killed, and when Fred died and George was left alone.
— Quora user Tanya Wheadon
Hedwig. She was one of the characters established early on in the series (even if she was extremely minor and obviously had no dialogue outside of noises). And while there were other deaths that were much more tragic, everyone else, from Dobby to Sirius, got a certain amount of emotional pause and heft to their passing, which allowed the characters (and the reader) to process grief. Hedwig was shot out of the sky, and Harry got absolutely zero seconds to react to it before he had to continue fighting for his own life, even having to destroy the side car with her body. There wasn't much consolation afterwards either, in my opinion. Her death seemed to lack the reverence it deserved, and that was devastatingly jarring to me when I read it the first time.
— Quora user Matt Becher
For some reason I always thought Hedwig's death was the saddest. She and Harry were mad at each other before she died, and Harry was so distraught by it, and the poor thing screeched and fell to the bottom of the cage like a stuffed animal. Makes me cry every time. She was with him in his lonely summers at Privet Drive. Her body was never found, and her death didn't get much recognition because it was then overshadowed by Mad-Eye Moody's death.
— Quora user Claire Richards