I think maybe another reason Dream got so upset during the meeting in 1889 was because Hob finally confirmed that he would never just wake up one day and want to die. Of course, Dream had seen proof of this after centuries, but this time was different. Not only did Hob admit that "I don't think I'll ever seek death," but he also called Dream out on the fact that Dream knew that, and that seeing if Hob wanted to die yet was no longer the reason he continued to meet him.
So not only did Hob call him out on being lonely, he also made him realize that he wasnt going to be leaving, like, ever. This is now a committed relationship whether you want to admit you're my friend or not because you've agreed to meet me here every hundred years and I'm not going away.
So then naturally Dream, in a state of panic, had to find a way out because maybe he never thought Hob would be a consistent thing anyway and now not only does he care about this human but he's also just been faced with the fact that he can have him forever and holy shit that is scary