Katherine's short temper is easily triggered in the early parts of the play. In act 1, scene 1, she seems to be angrily shouting at anyone within earshot and for no particular reason. When her father Baptista and her sister Bianca attempt to part from her company, she is even more enraged and insulted.
In act 2, scene 1, Katherine heckles Bianca regarding which of Bianca's suitors she loves most, not in a playful manner, but in a rather nasty, even abusive, one. When Bianca attempts to leave the room, Katherine gets angry and tries to run after her in a potentially violent rage. Later in the scene, she physically strikes Petruchio when he comes to woo her, right after she realizes her nasty words do not curb his innuendo-laden banter. Her physical violence is the most extreme manifestation of her temper.
There are multiple further instances of Katherine's short temper in the text, but no one agrees as to why Katherine is so angry. Some theatre directors interpret Katherine's temper and rage as resulting from being objectified as nothing more than a product on the marriage market. Her short temper becomes a way of lashing out against gendered expectations and a world that limits her because she is a woman.