Why is Severus Snape so popular

Why did Severus Snape present himself to Harry as angry?

Severus wasn't mudblood. He was a half-breed with a pure-blood mother of the Prince line; The half-blooded prince.

Lily was a childhood friend, a crush, and most likely the bitter man's only true love. He was telling Lily about magic and she was probably Snape's best friend for most of his (early) life.
When they became estranged later in her career at Hogwarts and Lily became romantically involved with James Potter, Snape developed a bitter resentment. He fell into the wrong crowd and joined the Death Eaters at the height of their power.
As Sibyl Trelawney Dumbledore at Hog's Head the prophecy 1 gave, Snape listened at the door and heard the first two lines before he was caught.

"The one with the power to defeat the Dark Lord is approaching ... Born to those who opposed him three times, born when the seventh month dies ..."

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

When Snape realized that he had made Voldemort focus on Lily, James and baby Harry, he panicked. While begging for Lily's life, he probably wasn't too worried about James Potter. Snape confessed to Dumbledore, expressed remorse, and stepped back on the side of the Light as a spy for the Order of the Phoenix.

When Harry arrives at Hogwarts a decade later, Snape reveals that he fundamentally hates Harry; Harry looked like a copy of his father, who was Snape's tyrant.
Harry had a habit of breaking rules:

  • second year stealing from Snape's stores
  • fighting trolls
  • sneaking around wearing an invisibility cloak
  • Even allowed Sirius Black to flee as soon as Snape 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 is taking care of Harry Has . While caustic and unfortunate as an educator, he looked after Harry, banned a broom curse for the first year, and all of his spy deeds to bring down Voldemort.

Snape was a spy. Most of the Slytherin students were children of Death Eaters. Like Dumbledore, Snape anticipated the rise of Voldemort as an opportunity. He had to keep his position as a spy. Playing well with Hufflepuffs, and especially Gryffindors, would have damaged his image, especially with the Death Eater parents.
He presented himself to be connected to the dark side because that was his job as a spy. He had years to ingratiate himself with them and even become Draco Malfoy's godfather.

In summary, Snape is so mad at Harry, especially because he's petty in a sense; to punish the son for the sins of a father he never knew. He's wild with the other Houses and is only nice to his Slytherins because he has to keep his spy role.