Zoey really hates her step-dad… and from what we see of him, this seems pretty justified. First off, he's "a fake. He fakes being a nice guy. He fakes being a good husband. He even fakes being a good father" (2.2). Basic math tells us that if he fakes being good, he's actually pretty bad. Ugh.
So what makes him such a terrible dad? For starters, he blames Zoey for being Marked, even though it's scientifically impossible to tell what will trigger the Change. He tells Zoey: "I told you that your bad behavior and your attitude problem would catch up with you. I'm not even surprised it happened this soon" (3.9). And when Zoey tries to explain the science behind it, he shuts her down: "God's knowledge surpasses science, and it's blasphemous for you to say otherwise, young lady" (3.15). Wow. We bet he's tons of fun at dinner parties.
According to Zoey, he gets away with all this hypocrisy because of how normal he looks: "He looks like every other dad-age guy. He has dark hair, skinny chicken legs, and is getting a gut. His eyes are like his soul, a washed-out, cold, brownish color" (3.3). Normal on the outside, soulless on the inside. It's no wonder she doesn't like him.
His response to the situation with Zoey's Mark is to see if their family psychologist will make a house call and to activate the prayer tree for their local church. Both these solutions don't address the urgent fact that Zoey is sick and needs to get to the House of Night stat. Zoey finally recognizes, though, that this is all about control, which her step-dad cares about more than anything:
He didn't want to lose his precious authority and the illusion that we were the perfect little family […] John had to preserve the illusion, and if that meant allowing me to get really, really sick, well then, that was a price he was willing to pay. (3.31)
So it sounds like Zoey's step-dad is a total skeezeball who cares more about the illusion of perfection than about the welfare of his own family. We're with Zoey in disliking him, and it's no wonder she leave the house he rules over behind without hesitation.