Well, it comes from a political divide within the elites, with Christians being blamed and killed for the material degradation of the empire, which was caused by material and bureaucratic failures of the 3rd century (classic othering) and then that cult was subsequently uplifted by other elites in opposition because it had become a populist response to the bungling elite class, thus taking the religion of widows, slaves, and freedmen and making it the religion of kings. It is likely a part of a Striestand effect, if another cult had been as persecuted, they might have been the saviors of the empire. Hell, if Judaism hadn't been so well incorporated into the empire at that point, it could have been Judaism.
Mind the biggest problem that Constantine had with the Christians is that they still hadn't stopped having their own bloody internecine conflicts, hence the need to create the Nician Creed.