Sword Saint Meng had little care about the greater good of mankind or anything of the sort. What really mattered to her was just those whom she cared about, and if anyone dared to hurt her precious child, she would pit her life against that person.
The reason she had eventually relented was due to those words reassuring her.
As a mother, it was inevitable that she would bear great ambitions for her child's future. With Yang shi volunteering to assist in the process and her husband reassuring all of her fears, she had eventually caved in.
Otherwise, given her strength, no matter how powerful Hu Yiwei was, there was no way he could possibly have planted the Innate Fetal Poison in her successfully.
In order to make more contextual sense, I named it Hundred Schools of Philosophers, but it's actually in reference to the Hundred Schools of Thoughts. Basically, it refers to the many different philosophies that rose during the Spring and Autumn period in ancient China. Two notable examples of the Hundred Schools of Thoughts would be Confucianism and Legalism.
Just to share a bit more since it's something that I'm interested in, Confucianism dictates the roles that each individual has to take within a society in order to society to function well. For example, a parent has to take the role of educating his children; a subject should remain loyal and obedient to the emperor; the emperor should rule wisely over his people, so on and so forth.
On the other hand, Legalism believes that human nature is selfish and the only way to maintain order was through strict enforcement of law. As such, maintaining societal welfare came well above the welfare of individuals.