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even people with the same language fight against each other sometimes (Civil war)
Many wars are caused by disagreements over ideology, politics, and many other issues which having a shared language would not affect.
To create peace it is necessary to solve the problem of conflict, the problem of social order. A way to solve this problem is private property, but private property by itself cannot guarantee peace. (continued in the next premise)
Common language is the lubricant to easy and manageable trade. Without a common understanding of costs, qualities, and explanation of products, trades are much more difficult to process and accept. It is easier to confuse a transaction or commit deceit when translations are poor due to translators.
it would reduce the "us vs them" mentality
Global language shift wouldn't be peaceful. How the one, universal language should be chosen?
Even within one language today we see racism. We also find murder, rape, torture etc. amongst communities who speak the same language. (usa for the racism example or french in regards to former french colonies)
One of the greatest difficulties that mankind faces is the transmission and representation of pain. Without proper techniques and procedures, it is difficult to explain one's pain so that we may feel it. Even within a common language it may be difficult to gauge another person's pain.
There would very quickly be mutually unintelligible dialects which would function as entirely different languages.
It would probably deprive us of the culture that is deeply intertwined with the language. Auxiliary languages have no culture except that of the creator.