Strangely, we're right in the middle of studying different views of divorce during the Second Temple Era in one of my history courses. The topic is a specialty of the professor teaching us.
The core issue seems to be that there was a debate at the time whether divorce was allowed or not. Some people, like Jesus, thought that the Torah allowed divorce only because of the low spiritual level of the Israelites at the time, but when striving for a higher spiritual level, one should not divorce. The reason being that when man and wife marry, they become spiritually one, returning to the way man and woman were created in Genesis, as a
unified entity. This unity is not something that may be reversed, not even through divorce, for they become "one flesh". Flesh cannot be divided without harming it.