By that logic of pride, Pakistan should have launched a full attack on India after 1971 debacle. But, it didn’t because wars aren’t started for pride or bluster. So, I disagree with the premise of an attack based on your assessment of loss of pride.
Moreover, there was no loss of pride. Loss of few fighters was a tactical setback and mature nations accept them in their stride. Even a sportsperson knows how to take losses and gains in a sports match.
It was a tactical setback, to which India changed the tactics and we know what it did to your bases from 8-12 May, while there was nothing to show for Pak side after the first day.
So, a war is likely, but for bigger reasons not childish ones.