She doesn't have a rich backstory. There is no reasoning behind her actions, nothing we can use to excuse her behaviour. She just seem to be purely evil.

That is, until we examine her actions.

Well, her most memorable physical characteristic is her love of the colour pink and kittens, and she dresses accordingly. There is nothing evil about this in anyway, yet it evokes a gut-reaction of disgust in most.

You could argue that some people just despise femininity, and that this is no different, but it's generally accepted that it's the contrast that people loathe, the hypocrisy of it; the smiling puppies and torture, pink ribbons and punishment.
So before her personality was revealed, she was already on bad footing.

Some of her early grievous offences include being rude to Dumbledore as he welcomed her to the school.
Malfoy has been noted for ignoring Dumbledore's speeches too, but he does not get any backlash for it, unsurprisingly.
But that is only the beginning.
Then, she goes to inspect the other teachers. Bear in mind that this is her job, she is paid to do this. She decides to put two teachers on probation.

One is clearly unqualified for the job, and seems to only have got in based on the fact that her great grandmother was good at the subject. That is not sufficient for her, nor should it be for anyone. She rightly does not understand why she is vilified for this.

The second teacher is a man. He has put his students in dangerous situations, has paid no attention to the curriculum, and some of them have even confided in her, saying that he scares them. He has turned up to class bruised and bloody, and seems to relish in situations when his students are in danger.

Putting him on probation was the sensible option, the reasonable thing to do.
Some vouch for his character, but that's not important. She doesn't care how good of a person he is, she just wants to know can he teach. Perhaps this is a shortcoming in her, but she doesn't see it that way.

Some one needs to take control of this school, and she thinks it should be her. She seems to be the only one who can look at things critically, without romanticising the whole affair.