Actually, strictly speaking, there was no deep-seated hatred between Nuwa and Houtu. Unfortunately...
Both of them were a little... petty.
Back then, Nuwa had been the first to become a Saint. Immediately after finishing her sermon, she announced that she would establish the Demon Teaching and the Witch Teaching, claiming a share of heaven and earth's destiny to bring the Witch and Demon races under her governance.
Nuwa's thinking at the time had been: With my standing as a Saint and teaching leader, I can govern both races, ease their conflicts, avert war, and preserve peace in the Primordial World.
Honestly, there was nothing wrong with that. Unfortunately, Nuwa had failed to consider how the two races felt and had overestimated her own abilities.
Even as a Saint of the Heavenly Dao, she remained so fragile and powerless before the surging tide of events. In the end, Hongjun intervened and confined her to Taisu Heaven, where she could only leave once the Witch-Demon Calamity had ended.
Thus, her plan to prevent war between the two races failed. Besides that, she had also offended Houtu over it.
Houtu remembered this even after attaining primordial unity. When Fuxi reincarnated, she tampered with the process and made him reincarnate as a Witch-Human. This infuriated Nuwa so much that she wanted to storm into the Netherworld and settle accounts with her.
But Nuwa was a woman of dignity. She could not lower herself to go to the Netherworld and quarrel with Houtu in person. She certainly wanted to fight, but things had not been as serious then as they were now, and an all-out brawl between two supreme goddesses would have been inappropriate. So she swallowed her anger and held back for the time being, merely keeping the matter in mind and planning to