The Ramban explains why the prohibition of marrying two sisters brought on this daf only applies during the lifetime of whichever sister he married first. Since two sisters should live in love and harmony, never strife, it is not proper for them to be competitors for the same husband. Of course, no Jew should fight with his fellow.
Rav Nosson of Breslov writes that the discrepancy between the solar and lunar calendar represents machlokes, strife, since the two systems are naturally at odds with one another and must be reconciled. Declaring a second Adar so that the two calendars can be aligned is a means of repairing their—and all other—rivalry. It is specifically in Adar, when the descendants of Amaleik sought our very lives yet we were victorious, that we have the power to settle all conflicts by declaring an extra month.
What this teaches me on the personal level is that a leap year, when a month is added, is an especially auspicious time to work on our unity with others. We can consider the devastation that is caused by controversy and work to dispel discord. We all believe that Hashem bestows life for a purpose, but when it comes down to our challenges with other people, it’s all too easy to forget. When we feel frustrated with family, friends, or fellow Jews, we need to remember that our real problem is with the One who created the person who is getting on our nerves. Since a second Adar imparts the gift of a double-measure of joy, we become better able to work on fixing broken relationships during the second half of a leap year (Likkutei Halachos, Birchas Hareach U’Birchas Pratios 4:12 and Arba Parshiyos 1:1).