She didn't personally hate him. She was just trying to do her job and quite honestly she was a bit mean.
Wikia Dolores Umbridge:
Umbridge was also a cool-demeanoured sadist who rarely expressed the
extent of her anger openly, casually making decrees and handing out
torturous punishments with a smile (most notably, forcing Harry to
carve "I will not tell lies" into the back of his hand with a Blood
Quill). She created several new rules and regulations in order to
increase control and chances to punish students, despite many of them
being ridiculous and unfair.
The Ministry sent her to do a specific job if she hadn't of completed it she would have been in trouble and would have lost some of her power. From the following quote we can see she wouldn't of liked that. She exerted her power to the full extent, I mean she did almost kill Professor McGonagall.
She was depicted using any means to maintain her personal power and
the political power of her bosses. She committed attempted
soul-removal (via the Dementor attack on Harry), solicited bribes, and
tortured children to achieve her goals.
And she even hated her own family.
Her younger brother was a Squib but she herself was born a witch.
Under her father's influence, she despised her Muggle mother and her
Squib brother, considering them inferior to her and her father, and
they both denounced them.
It really wasn't just Harry she hated everyone who didn't have power to stop her. It was because she felt bad about herself.
Following Voldemort's takeover of the Ministry of Magic in 1997,
Umbridge resumed her post as Under-Secretary and oversaw the
registration and persecution of Muggle-born witches and wizards. She
conducted trials with sadistic pleasure, subjecting innocent
Muggle-borns to the presence of Dementors and sending them to Azkaban
for supposedly stealing magic from "real" witches and wizards
Cos Forums has some interesting takes on it.
From User Fellyphone:
I think the original reason why Umbridge had a beef against Harry had
to do with her wanting power and she saw Harry as a threat because he
associated himself with Dumbledore. Rather than get rid of Dumbledore
right away, she sought to discredit Harry and to wreck havoc on his
summer by sending out the dementors.
Harry would never shut up about what happened and that undermined her authority since she was suppose to "stop lies" and do the Ministry's bidding.
From User Saiorri:
I think like a lot of other people, especially the ones who wanted to discredit Dumbledore, Umbridge wanted to silence Harry just
to prove he's human and not "The Chosen One." Umbridge didn't have to
know Harry to discredit him. He was trying to tell everyone that LV
was back, when the Ministry was saying LV was a done deal from over a
decade ago. I was just talking to my mother about this the other day.
Imagine, if you will, that we didn't know that Hitler shot himself
instead of being defeated by his last victim, and we didn't have a
body to prove he was gone, and then some kid claims "Hitler" did some
murders in Israel in 1958 and he was there-----if you lived in Israel,
would you want to believe he was back?!?! ......