Why did Severus Snape present himself as evil to Harry?

Snape as a person was not very friendly or social, for that matter. His anger had a lot to do with his troubled childhood. He was a halfblood, had parental issues and was thoroughly bullied by James and Sirius at Hogwarts. This led him to develop a tough exterior.

However, Severus loved Lily deeply and had a fair share of affection for Harry too. But in Harry he saw James, a person who was used to being popular and treated as hero, and someone with utter disdain for rules.

In the end, Snape sacrifices his life for a cause and for Harry. The only reason he created that friction between himself and Harry was because he wanted Harry to be distant.

From Snape's point of view James Potter had everything easily. He was rich, popular, clever, charismatic and he had Lilly and he made sure he rubbed Snape's face in it. The girl who Snape deeply loved had loved the man whom he hated after suffering years of persecution by him,

Snape was torn. He 'loved' Harry in a way due to Lilly but every time he saw him he was reminded of his feelings for Lilly and Lilly's feelings for James. He also seemed to find Harry reminded him of his father whom was someone Snape hated. Hence he probably did not like Harry either.

Every second he spent dealing with Harry or with Harry on his mind was deeply emotionally wounding. It is impressive he remained as composed as he did.

Severus was not a mudblood. He was a half blood with a pureblood mother from the Prince line; The Halfblooded Prince.

Lily was a childhood friend of his, a crush, and most likely the bitter man's one true love. He told Lily about magic and she was probably Snape's best friend for most of his (early) life.
When they became estranged later in their Hogwarts career, and Lily became romantically involved with James Potter, Snape developed a bitter resentment. He fell in with the wrong crowd and he joined the Death Eaters, at the height of their power.
When Sibyl Trelawney gave the prophecy¹ to Dumbledore at the Hog's Head, Snape was listening at the door, overhearing the first two lines before being caught.

"The one with the power to vanquish the Dark Lord approaches...Born to those who have thrice defied him, born as the seventh month dies..."

This gave Voldemort all he needed to narrow down which two children it could be; Neville Longbottom or Harry Potter.

Once Snape realized that he had caused Voldemort to focus on Lily, James, and baby Harry, he panicked. While he begged for Lily's life, he probably wasn't too concerned about James Potter. Snape confessed to Dumbledore, expressed his remorse, and rejoined the side of the light as a spy for the Order of the Phoenix.

When Harry arrives at Hogwarts a decade later, Snape shows that he hates Harry on principle; Harry looked like a carbon copy of his father, who was Snape's bully.
Harry did have a habit for rule breaking:

• stealing from Snape's stores in the second year
• fighting trolls
• sneaking around with an invisibility cloak
• even allowing Sirius Black to escape once Snape had caught him.

This made it easier for Snape to see more of James in Harry, and less of the intelligent Lily Evans who was a dedicated student.
It should be noted that Snape did watch out for Harry. While he was caustic and deplorable as an educator, he did look after Harry, locking a broom jinx in first year, and all of his acts as a spy in bringing down Voldemort.

Snape was a spy. Most of the Slytherin students were the children of Death Eaters. Like Dumbledore, Snape anticipated the rise of Voldemort as an eventuality. He needed to preserve his position as a spy. Playing nice with Hufflepuffs and especially Gryffindors would have hurt his image, especially with the Death Eater parents.
He portrayed himself as aligned with the dark side because that was his job as a spy. He had years to ingratiate himself with them, even becoming Draco Malfoy's godfather.

So in summary, Snape is so angry with Harry in particular because he is petty in a sense; punishing the son for the sins of a father he never knew. He's ferocious with the other houses and is only nice to his Slytherins because he needs to preserve his role as a spy.

" I could not understand why he portrayed himself as angry, ferocious, tough and mischievous to his students? "

• First, among other things, because he was a high-IQ, low-social-IQ geek, who had to develop a tough bullying exterior to survive all his life.

  He clearly hated incompetents (thus total offense at Neville's entire existence). He disliked Gryffindors since he saw nothing but grief from them all his life.

  He doted on his in-group (Slytherins) - clearly illustrated when he forsake Lily and her love for being with his budding-DE Slytherin friends when in school.

• Second, because that tough pro-Slytherin image was helpful to him as far as convincing Death Eaters that he was still on their sides. He was "in" with Lucius Malfoy and other Slytherin DE parents, and playing favorites helped him in that even if he wasn't naturally inclined to do so, which he was (see #1)

He always treated Harry and the students in a way which cause everyone to dislike him, except for his Slytherin students.

Was it because he could not get Lily and that Harry was the son of James, the hater of Snape? Why did he pretend to be so?

Well, apart from not being very friendly at all, Severus loved Harry in a strange way. He was the son of the woman he loved his entire life, and that's why he protected him. But from the moment he met Harry, except for his eyes, he was a mini-copy of James. Everyone told him that he was a little copy of James but had his mother's eyes. So seeing "James" all around was really difficult for him after all he's been through. Especially when little Harry opened his mouth and became a little sassy. Severus had the upper hand this time though, and that's why he was a little 'cruel'. Don't forget that when we read about Snape finding out about Lily's death and the survival of her son -- Harry -- he said that he wanted to do anything to protect her and not her child or husband. Those were words of grief though, and once more, Dumbledore reasoned with him and he managed to protect Harry until his last breath.

James Potter bullied Severus Snape during their year in Hogwarts, so naturally, Snape developed a disliking for him. And also, he was head over heals with Lily but the girl whom he loved deeply, had chosen James over him. Harry is Lily and James's son, he behaves like his father and his hair is messy like his father's but he has his mother's eyes,thus whenever Snape sees him, he is reminded of Lily and James, but Harry broke a couple of school rules, which reminded him mostly of James, whom he despised instead of Lily, whom he loved.

Snape was dealt a bad set of cards. His childhood best friend falls in love with, who he considered, a rich pompous bully. It's his fault that Voldemort interprets the prophecy by Trelawney to mean that Harry will be his downfall. He essentially signed Lily's death warrant. Guilt and remorse motivates him to protect Harry but I think years of working undercover (which probably included torture and murder) changed him. The life of a double agent must be lonely. When Voldemort comes back after his demise, he's asked to return to the dark ranks. He's bitter and alone.

The movies don't depict the actors ages correctly. Snape becomes a Death Eater after school (around age 18) and his best friend dies 2 years later. He'll have about 10 years of peace before he returns to espionage and dies at age 38.

Snape's role during this entire time was extremely sensitive and required master espionage and image-control skills. As he and Dumbledore anticipated that Voldemort would return eventually, and many of Snape's actions would be reported on by Death Eater spies or gained through torture and Legilimency, even if Snape's true mentality and intentions were inaccessible to the Dark Lord, he had to consider every decision and relationship carefully. He treated Harry Potter with maximal coldness and never missed an opportunity to cause him trouble, as any variation from this would have cast suspicion on him in Voldemort's eyes.

Taken from Harry Potter Wikia