Actually the primary reason he never argued for divorce was that in his day, divorce was actually super easy. During his day there were two schools of thought on divorce; one required specific grounds for divorce (which included adultery, abuse, and abandonment); the other allowed it for "any cause". There's a case to be made that Jesus' teaching on divorce (most fully represented in Matthew 19[1]) was aimed exclusively at the unfair use of this "any cause" divorce [2].
[1] https://www.biblegateway.com/passage/?search=Matthew+19%3A1-...
[2] http://www.instonebrewer.com/DivorceRemarriage/Articles/Whit...