For peace of mind, many families often arranged marriage matches for their children at a young age; infant engagements were not rare instances in those times.
Zhuang Yuanren was considered a treasure by Zhuang Ruman and Mrs. Song, he was not easily satisfied with ordinary girls, so it might be possible for them to pre-arrange a marriage for Zhuang Qinghe too.
Moreover, Zhuang Qinghe is a girl; once the betrothal is arranged, if all goes well, the groom's family would need to present betrothal gifts to the bride's family. And Zhuang Ruman's family, being in a tight financial situation currently, could benefit from this…
The motive behind arranging a betrothal for Zhuang Qinghe is self-evident.
Although Mrs. Song is harsh, she isn't very thoughtful and is affectionate towards her children. This matter probably wasn't her idea, it would likely be the cunning and self-serving Zhuang Ruman who may have come up with this plan.