I have looked at many universities and seen how in English speaking countries, their mottoes tend to be written in Latin. What was the first college/university in an English-speaking nation-state (England, Ireland, etc.) to use Latin for their motto and what was their reasoning for doing this?
The oldest universities in today's English-speaking world are Oxford and Cambridge, having mottoes Dominus illuminatio mea, "The Lord is my light", and Hinc lucem et pocula sacra, "From here, light and sacred draughts". These mottoes, as LangLangC pointed out, are not as old as the universities themselves. Mottoes often accompany coats of arms, which the two universities acquired in the 16th century.
Why are they in Latin? Latin was not only a prestige language, but the language of academia and learning throughout the Middle Ages and indeed into the Modern Era. Putting the motto of an establishment of learning in a vulgar local tongue would hardly have made sense at the time. Knowledge of Latin was an entrance requirement at Oxford up until 1960, according to Wikipedia.
NB that the royal motto of England itself, Dieu et mon droit, is older and in French.