Question: Why is it forbidden for a woman to remarry an ex-husband after having married someone else for period of time?
Answer: Rabbi S.R. Hirsch (Deuteronomy 24:4) observes that there can be nothing legally wrong or immoral with either the first divorce, or the second marriage and its own subsequent divorce. Why then, he asks (precisely as you do), does the Torah forbid the first husband from remarrying his original wife?
Finding ingenious textual evidence, Rabbi Hirsch suggest that with this law, the Torah attempts to forestall any corrupted abuse of the holy marriage institution: Should a couple wish to engage in a reprehensible cycle of “wife-swapping” – but with the imprimatur of legality – they could collude with another man to plan a set of divorces and marriages to facilitate their desires.
By forbidding this remarriage, this avenue is blocked. Could this potentially have caused harm to a perfectly innocent couple who made an honest mistake? Perhaps. But I am sure that the knowledge of this law has made many other mildly dissatisfied couples give every ounce of extra energy they had to make their existing marriages work – thereby further sanctifying marriage in general.
I hope this helps,
Rabbi Boruch Clinton