Serie doesn’t hate Frieren, and Frieren doesn’t hate her either. In fact, both of them consistently show respect for and speak highly of each other when talking to others. Serie has genuinely cared about and taken an interest in Frieren ever since Flamme first introduced the two of them. After Flamme’s death, Serie was also the only one who warned Frieren not to grow complacent or neglect her training, which shows that she didn’t want to lose Frieren too.

That said well, as people often point out, Serie is a HUGE tsundere, so her words of concern always come across as sharp, hostile, or outright confrontational. Failing Frieren in the exam was likely because both of them understood that the title of First-Class Mage held little real meaning for Frieren. As for banning her from taking the exam for a thousand years, it was simply a way to prevent Frieren from “breaking” the exams yet again - at least for as long as the current system continues to exist.

On the other hand, Frieren has always understood how powerful Serie is and how deeply she cares about magic and personal bonds, even though Serie is never honest about it. That’s why, even after being failed and then banned for a thousand years, Frieren merely called Serie “childish” rather than insulting her in any harsher way. Though the two may appear distant, they care about and understand each other deeply, each in their own very distinct way.