She always does anything to humiliate Lizzie and her friends, Miranda and Gordo, and also make fun of them whenever they do something "childish", like when she saw them at the live show of "Clover and Daisy's Magic Train", when Kate took her little cousins there.
She can be very unlikable at times. For example, in "You're a Good Man, Lizzie McGuire", while she and Lizzie were working together for the Spring Fling committee, she knocks over the bust of the school's founding principal. She was never caught, and the principle canceled the dance unless someone confesses. Kate never does, meaning she doesn’t even care about the dance and just likes to see someone suffer. Because eventually, Lizzie decided to take the blame to save the dance.
She is shown to be very greedy in some episodes like "Misadventures in Babysitting", where she looks after a baby just to get paid, and as seen during that flashback, she did a terrible job as a babysitter. Even Lizzie is a better babysitter, as Lizzie actually took good care of Matt during that episode and even protected him when they thought a criminal was breaking into their house. Kate, on the other hand, had a fire while babysitting, didn’t even notice it, and didn’t bother to check on and save the baby.
She can be bossy at times.
She’s shown to be not caring about a child in her school, as while she did see Matt in "Lizzie's Nightmares" at her school, like many of the other students, she didn’t mind and got along with him. Who know? Two of the most unlikable characters in the show actually getting along, and keep in mind that Matt is Lizzie’s, the girl Kate always picks on, brother.
She’s shown to even work with some of her classmates, other than Lizzie, Miranda and Gordo, into doing bad things with her, like with Ethan in "I Do, I Don't", while they were paired with different partners, Larry and Miranda, respectfully, they planned on abandoning them at the reunion during the assignment. Ethan is normally a dumb but very nice guy, but she made him pretty unlikable in that episode.
She is very stubborn.
As the series went on, she started becoming less unlikable and getting more character development.
It was revealed she used to be friends with the main characters, before she became popular, and its shown that she helps them sometimes, especially when they have to work together.
She does have her funny moments, like whenever she gets karma for her bad actions.
Speaking of which, it’s always satisfying whenever she gets comeuppance for her bad actions, like when falling for Matt’s pranks, and when Lizzie stands up against her actions.
Deep down, she does care about Miranda, Gordo, and especially Lizzie, as she’s seen sometimes working together with them and even having fun with them.
Lizzie McGuire and The Lizzie McGuire Movie would most likely not be as great without her.
Speaking of which, The Lizzie McGuire Movie is where she was at her best, as she helped Lizzie with her popular status in Rome, and even encouraged her to go on for Gordo after he took the blame for Lizzie. And she is also seen cheering for Lizzie when she finally got over her stage fright, and had a good moment when she was eating with Ethan, thinking about Lizzie being popular now and saying she doesn’t know everything, and Ethan lightening her spirits saying it’s ok for a girl to not know everything, making her happy.