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I think there are two basic answers to your question. The first, and simple answer is:
The more direct, and also more complex, answer to your question is:
As Matthew 19:18 states,
Jesus is clearly pointing out that divorce is, in fact, legal. It is bad, but it is permissible. To turn it into an iron-clad law is then much like laws concerning the Sabbath - Jesus values the individual over the institution, even an institution as great as marriage.
(Note: Not advocating, just explaining the rationale!)
I think that the biggest issue is the exception in Matthew 5:32:
The Catholic Church takes that phrase to mean, "except in the case of unlawfulness" (which is why there is an annulment process), but many take it as an "out." Regardless of the merit of such an interpretation, it seems that that "escape clause" has been used a bit more than it should be.
some Protestant denominations, like Anabaptists, are as negative about divorce and remarriage as are Catholics.
to answer directly the title question, i might say that it's because of either
A. the Pauline exception
B. because of a practical and compassionate utilitarian ethic that understands if and when the earlier marriage is, in any possible context, salvageable or reconciliable. if there is no hope for the original marriage (like, perhaps, the other former spouse remarried a 3rd party) can be salvaged, they might think that nothing particularly good is being solved by a lifelong prohibition to marry.
and then if they remarry anyway, what should the church do in response? i have been involved with a church of repute that has literally excommunicated a member (who was the choir director and worship music co-director) for divorcing his wife and marrying another woman who was a former member of the church. i do not know what the consistent Protestant response to divorce is, and i wouldn't say that this one example is typical of Protestants, but it is Protestant while also more specifically Anabaptist.