A new popular fan theory is that Snape purposefully targeted and killed
to save Harry's life. Could Snape have purposefully targeted and killed
so their death wouldn't give Harry away in the ensuing fight in the sky?
Here's the "theory". A single Tumblr post that's been shared a lot:
Sooo the death eater that kills Hedwig is actually Snape, and he killed Hedwig so the other death eaters and voldemort wouldn’t know it was harry anD HE WAS ACTUALLY TRYING TO PROTECT HARRY THE WHOLE TIME OMG
Hedwig was seen when there were two Death Eaters pursuing Harry. She was visible and seen by both of them.
It was Harry's "signature spell" that gave away his identity. Hedwig could've been stored with any of them.
‘Expelliarmus!’ Harry yelled.
‘That’s him, it’s him, it’s the real one!’
The hooded Death Eater’s shout reached Harry even above the thunder of the motorbike’s engine: next moment, both pursuers had fallen back and disappeared from view.
This was followed by Voldemort making a personal appearance, because they knew this was the real Potter. It had nothing to do with the owl.
As otherwise mentioned, Snape was off casting Sectumsempra at one of the twins at this time.
Here, Hedwig gives away the real Harry by protecting him from an Avada Kadavra aimed at his persons. There's only a single Death Eater around at this point, but as soon as Hedwig intercepts the death spell, the Death Eater backs off.
The plot in the movie is that Hedwig's appearance tipped of the true Potter, and the retreating Death Eater then alerted Voldemort, who then appeared. Only a single Death Eater witnessed Hedwig's appearance. Voldemort appears immediately after.
Were it Snape to have killed Hedwig, to protect Harry, Voldemort wouldn't have shown up.
No, this theory holds no water for either the book or film version of events.
It was all confusion. I seriously doubt that Snape would have risked hitting and killing Harry.
Screams, a blaze of green light on every side: Hagrid gave a yell and the motorbike rolled over. Harry lost any sense of where they were. Streetlights above him, yells around him, he was clinging to the sidecar for dear life. Hedwig’s cage, the Firebolt, and his rucksack slipped from beneath his knees –
“No – HELP!”
The broomstick spun too, but he just managed to seize the strap of his rucksack and the top of the cage as the motorbike swung the right way up again. A second’s relief, and then another burst of green light. The owl screeched and fell to the floor of the cage.
“No – NO!”
The motorbike zoomed forward; Harry glimpsed hooded Death Eaters scattering as Hagrid blasted through their circle.
Hedwig was in a cage, as was clear in the last quote.
So killing the owl wouldn't have helped prevent "so she wouldn't give Harry away in the ensuing fight in the sky", therefore the motivation in the fan theory doesn't make any sense.
Also, Snape ended up fighting Lupin and George, and the pairs all split up immediately, so Snape couldn't have had too much time to attack Harry (or the owl) at that time:
“He lost an ear,” said Lupin.
“Lost an—?” repeated Hermione in a high voice.
“Snape’s work,” said Lupin.
“Snape?” shouted Harry. “You didn’t say –”
“He lost his hood during the chase. Sectumsempra was always a specialty of Snape’s. I wish I could say I’d paid him back in kind, but it was all I could do to keep George on the broom after he was injured, he was losing so much blood.” (DH)
In addition to DVK's answer (i can't comment yet!), as far as i'm aware, Snape wasn't aiming to kill and not using the killing curse. Aiming on a broom/in flight was too difficult, and resulted in him accidentally cutting off Georges ear with Sectumsempra
A Death Eater moved ahead of Snape and raised his wand, pointing it directly at Lupin’s back. "Sectumsempra!" shouted Snape. But the spell, intended for the Death Eater’s wand hand, missed and hit George instead -