Bdtyktl

We know that Voldemort is a half blood. He also hates half bloods, we can see this from Harry Potter and the Half Blood Prince (Movie). When he takes command he starts killing half bloods as well.

What is the reason to hate half blood even if he was a half blood?

He doesn't?

I'm not entirely sure what you mean by "Harry Potter season 6", but there is no evidence that Voldemort was specifically targeting half-bloods. While he certainly considered pure-bloods to be of a higher standard, he didn't even hide his half-bloodedness from the Death Eaters - he is telling the story of his parents to Harry as the Death Eaters arrive (so they can hear him as he's talking to Harry).

Voldemort laughed again. Up and down he paced, looking all around him as he walked, and the snake continued to circle in the grass.

"You see that house upon the hillside, Potter? My father lived there. My mother, a witch who lived here in this village, fell in love with him. But he abandoned her when she told him what she was.... He didn't like magic, my father...

"He left her and returned to his Muggle parents before I was even born, Potter, and she died giving birth to me, leaving me to be raised in a Muggle village... but I vowed to find him... I revenged myself upon him, that fool who gave me his name... Tom Riddle...."

Still he paced, his red eyes darting from grave to grave.

"Listen to me, reliving family history...." he said quietly, "why, I am growing quite sentimental... But look, Harry! My true family returns..."

The air was suddenly full of the swishing of cloaks.

[...]

"I knew that to achieve this - it is an old piece of Dark Magic, the potion that revived me tonight - I would need three powerful ingredients. Well, one of them was already at hand, was it not, Wormtail? Flesh given by a servant...

"My father's bone, naturally, meant that we would have to come here, where he was buried. But the blood of a foe...["]
_{Harry Potter and the Goblet of Fire, chapter 33: "The Death Eaters"}

And he had half-bloods in his innermost circle, such as Severus Snape.

Half-bloods were allowed to keep their wands in Harry Potter and the Deathly Hallows, while Muggle-borns were not. The pureblood Wizarding community was so small, that if he had killed all half-bloods, the Wizarding community would soon die out, because there were so few people.

So, to answer the question "Why does Voldemort hate half-bloods?" - he doesn't; he just holds them to be lower than purebloods (but still higher than Muggle-borns).

In fact, he apparently doesn't want to kill even all Muggle-borns - seeing how many times he tells Lily Potter to "step aside". He says in Deathly Hallows that he doesn't want to spill magical blood:

"If you continue to resist me, you will all die, one by one. I do not wish this to happen. Every drop of magical blood spilled is a loss and a waste."
_{Harry Potter and the Deathly Hallows, chapter 33: "The Prince's Tale"}

And earlier in Deathly Hallows, we see that being a half-blood under Death Eater rule is better than a Muggleborn:

And then, abruptly and shockingly amid the frozen silence, one of the dungeon doors on the left of the corridor was flung open and screams echoed out of it.
"No, no, I'm half-blood, I'm half-blood, I tell you! My father was a wizard, he was, look him up, Arkie, Alderton, he's a well-known broomstick designer, look him up I tell you — get your hands off me, get your hands off —"
_{Harry Potter and the Deathly Hallows, chapter 13: "The Muggle-born Registration Commission"}

He is blood purist.

I am not completely sure about Mithrandir's opinion, that Voldemort didn't hate half-bloods, but it seems likely that he did hate them less than Muggle-borns.

I didn't evidence of his own opinion but at least his closest death eater Bellatrix made her opinion very clear (we can assume, that she got most of her opinions from Voldemort):

“Shut your mouth! You dare speak his name with your unworthy lips, you dare besmirch it with your half-blood's tongue, you dare”

^{― Bellatrix Lestrange, Harry Potter and the Order of the Phoenix}

Voldemort himself was a blood purist, he dreamed about having a wizard world with only pure-bloods, therefore any disruption of the blood purity was a matter of hate for him.

Also, Ron seems to think that half-bloods aren't exactly liked by the purist community:

“Dirty blood, see. Common blood. It’s ridiculous. Most wizards these days are half-blood anyway. If we hadn’t married Muggles we’d’ve died out.”

^{― Ron Weasley, Harry Potter and the Chamber of Secrets}

Also, I would speculate, but I think, that the fact he himself is half-blood only increased the hate inside him (and probably also towards himself). He wasn't exactly balanced person…