In May 11 1784 Emperor Joseph's language law was declared, replacing Latin for German as official language of all provinces of the Empire. This practically meant Hungary and Galizia as German was the language of other parts already. The law contains detailed reasoning, at least for the time: It posits the use of Latin as backwards, that not many can speak or write in it, that business isn't conducted in it. With regards to Hungarian the law says it isn't even majority language in Hungary (which was true at the time, as this is the era when post-Ottoman Hungarian lands, previously devastated were being re-populated by the Habsburgs: one source states Germans enjoyed slight plurality in Hungary for a time in the 18. century). In contrast German is already widely used and it will be efficient for the monarchy and business to have a single official language, and will also help bring the many people inhabiting the empire together. For Hungary it even adds that people should stop wasting their time learning so many languages and just focus on German. I'll include link to the whole text in sources. Starting November 1 1784 governing bodies, imperial offices switched to German while the Diet, counties and the judiciary system were supposed to do it within three years, and any public offical failing to learn German was to be sent off. Teaching, including within seminaries was also to be conducted in German.
This decision was in line with Joseph II's other aspirations, committed to reforms, modernization and centralisation with the ultimate goal of creating an enlightened absolutist state (Gesammtmonarchie) with him as the sole head , collectively known as Josephinism - abolition of serfdom, religious freedom, education and administrative reforms and so on. These made him a quite unpopular ruler amongst the deeply conservative Hungarian nobles, though he wasn't popular amongst many others in the Empire either, like in Austrian Netherlands and Lombardy. Only a few weeks before Joseph's death, the director of the Imperial Police reported to him: "All classes, and even those who have the greatest respect for the sovereign, are discontented and indignant".
Getting back to the language reform, it instantly caused great dissent among Hungarian nobles whom composed the Diet, albeit there was a small josephinist minority that supported it. The Hungarian chancellery added an addendum stating "our dear language is abandoned, unpolished and uncommon in our country". It further goes in by lamenting that Hungarian wasn't made by the old kings an official language, finally turning somewhat poetically hopeful that things will change and it will thrive again. The language reform movement was already ongoing at the time (typically dated to start in 1772 by drama written by György Bessenyei) but Joseph's reform gave it a serious kickstart with many nobles standing behind the cause and helping fund Hungarian language publications, newspapers and organizations. People like Ferenc Kazinczy, János Ribiny or János Molnár made up and popularized new words to replace Latin, Greek and German terms for science, literature, grammar and practically any field.
The law was only in effect till the death of Joseph II mere 6 years later, whereas in 1790 with the exception of the serfdom reform, religious tolerance and lower clergy support law he abolished all laws at his deathbed. A worn out, unpopular, broken ruler, it was probably his wish to make his legacy appear better to his people and to make his successors life easier. Just months after his death the first publication from the chancellory was in both Hungarian and Latin, urging to make Hungarian replace German and Latin in education and administration. However Latin still stayed the official language until 1844, for a variety of reasons: Hungarian barely held a pluralistic majority by the turn of the 19.century; much of the nobility wasn't Hungarian, and the language reform process was still far from finished.
Sources:
Encyclopaedia Humana Hungarica 06.
[The Law on German Language in Administration, M. Votruba] (https://www.pitt.edu/~votruba/sstopics/slovaklawsonlanguage/Austrian_Law_on_the_German_Langauge_in_Hungary_1784.pdf)