They are just letting out 7 years long frustration. They are saying things to each other that they should have said in peaceful way during their marriage.
N i don't think its Dev's male ego. He is just sad that his name is not associated with her anymore. Remember jab tak mera naam tumhare naam k sath juda hai sab theek hai.About their fights, i feel its important to spit it out rather than bottling it up inside.