By the mid-sixties, AD, downtown Rome was pretty much a dump. Most of the buildings were very old, and many of them were built of wood. There had been several calls for repairs and renovation, but to little avail. The sitting Emperor, Nero, had plans drawn up for a whole new downtown, made up mostly of public buildings: squares, baths, theaters, temples and so forth. But, he couldn’t get the Senate to go along with financing such a huge public works project. So, that’s one reason that some people have advanced blaming Nero for having the fires set. Some have even suggested that he sat in his palace above it all and played the lyre. Folks around here usually render that “Nero “fiddled”. But, there’s really no evidence of that, and there’s even some argument that Nero wasn’t even in Rome at the time. Of course, he could still have hired men to do it for him.
In any event, the fire started (or was started) in the thickly-populated, largely wooden area in the center of the old city, where there were both many shops filled with flammable merchandise (olive oil, cloth, hay and straw, etc.) and many tiny, twisting streets, which made it hard to fight the fire, once it started.

Whether Nero or somebody else started it, it quickly got out of hand, and ended up burning for six days. People then not being very different from people now, there was a huge outcry to find (and punish) those who started it. Nero finally hit upon the idea of blaming the Christians.
This was in 65 AD, remember. The Jews still enjoyed special protection from Rome because of their treaty. The Christians though, many of whom were Jews, enjoyed no such protection. The Temple Jews had disowned them. Furthermore, many of the Christians in Rome were slaves or foreigners, and thus had no social status to amount to anything. Indeed, many of them didn’t even want social status. The Church had been founded by and for “the poor”, and many of the practitioners were already trying to practice poverty as a lifestyle. They made the perfect scapegoats, and Nero was quick to take advantage of the fact.
Besides, Christian behavior was suspect, anyway: They avoided the large temples of the city and instead worshipped in member’s houses, or even in the outdoors. They avoided the Roman practice of burning their dead, and instead formed funerary societies, and buried bodies underground. Some even met in these underground cemeteries and worshipped by candlelight. It was easy enough to sell the idea that they might have started the fire, either accidentally, or, later, on purpose.
Nero was the first Emperor to blame Christians for a tragedy, but he wasn’t the last. Ten times, in the next two hundred and fifty years the Church got such blame, and had to endure the retribution of the Empire.