i don't know why he jumped out for the cat but i can say for sure that this teacher guy isn't any good, you can clearly see the differences between a good spirit and a real bad one in chapter 4(the author even clearly said that "don't judge a book by its cover", that alone even emphasizes what a good spirit should look like through the illustration of the thug guy's spirits), this guy is clearly haunted by the ill-intent spirits, not blessed by them, you can also see that he was haunted immediately upon encountering another "bad shaped* spirit in chapter 4 in his meeting with miko chan and her friend, that bad shaped spirit even cursed him to die right by his ear
Another example is miko chan's dad, even though he is spirit, he is in really good shape and blesses his family
if this teacher dies in this accident, i can only say that this is his karma, he pays for what he has done up till now, like, seriously, having a bunch of *bad shaped* spirits haunt you day by day, cursing you to die, his luck has been really something for him to live this long