After reading both Issue 4 of the comic and the story where we follow Xin Zhao and his reaction to Jarvan burning his father's letter which pertains to the fair treatment of mages in Demacia, the discussions around this have been interesting. I have seen plenty of discussions talking about the abrupt mood shift of Jarvan, and as up until now we have seen him as a more progressive figure in terms of allowing non Demacian things into the country. Now why would he be so angry against anything that does not align with Demacias Ideals? The answer is that HE CANT ACT ANY OTHER WAY.
Lets break down what just happened in Demacia:
1. Mage rebellion just happened, hating mages right now is now even more popular than ever.
2. Jarvan III just died, the general populace loved him as their king. This feeds into the hatred for mages even more.
3. With the Mage rebellion concluded, the Mage seekers will have EVEN MORE POLITICAL POWER within Demacia and can now go to more extreme methods to deal with mages.
Now lets go over why Jarvan IV had to burn his fathers letter:
1. If he did follow his fathers wishes, he would have a coup on his hands by the Mage seekers (Or the Crownguard, not too sure if they had a hand in killing his father). The style in which Jarvan III wanted the mages to be set free would not be possible due to what just recently happened due to the rebellion and the now reinforced purpose of the Mage seekers within Demacia.
2. It doesn't make sense that the King would now out of all times would suddenly decide to make a letter freeing all mages. And Xin and Jarvan IV both agreed, he was a very stubborn person. But the closest person who could possibly change his mind would be his son. The idea to free the mages was the Prince's idea from the start. This would be done by injecting this into conversations between when they were talking to each-other until the King made the idea his own.
In other words, Jarvan IV has to play the part of the grieving son to ensure that he does not die and that the vision that he and his father tried to achieve does not amount to nothing. He has to wait for an opportunity that will allow him to bring mages into Demacian culture while neutering the power the Mage seekers currently have within the country (and that opportunity is possibly going to come in either the shape of a small blond girl or a giant gargoyle statue, perhaps both).