It is time for opposition to the Annexation of Texas to cease.... Texas is now ours.... Let their reception into the "family" be frank, kindly, and cheerful (O)ther nations have undertaken ... hostile interference against us, ... h pering our power, limiting our greatness and checking the fulfillment of our manifest destiny to overspread the continent allotted by Providence (God) for the free development of our yearly multiplying millions.

California will, probably, next fall away from (Mexico).... Imbecile and distracted, Mexico never can exert any real governmental authority over such a country... The Anglo-Saxon foot is already on (California's) borders.... ?
armed with the plough and the rifle, and marking its trail with schools and colleges. courts and representative halls, mills and meeting-houses.... All this (will happen) in the natural flow of events...

How can this document be used to argue against America going to war with Mexico?

This document can be used to argue against America going to war with Mexico by emphasizing the idea that the natural flow of events will lead to the annexation of California without the need for military intervention. It suggests that the "Anglo-Saxon foot" is already on California's borders and that the "free development of our yearly multiplying millions" will be achieved through peaceful means such as the plough, rifle, schools, colleges, courts, representative halls, mills, and meeting-houses. This document implies that Mexico is too weak to exert any real governmental authority over California, and that war is unnecessary and would only serve to hinder America's power, limit its greatness, and prevent the fulfillment of its manifest destiny.