There's only one logical reason: Idealism. The Romans saw themselves as enlightened, educated, and happier than other peoples, and this conceit - it was in large part a conceit, as we know from historical records - drove them to try and rule the entire world.
In material terms the Romans were wealthier and more comfortable than anyone ever had been in the history of the world. Their technology, money management, labor and military organization skills were equal to - or even superior - to our own; but there was an aimlessness and unfocused aspect to their achievements. Once the Romans had attained creature comforts like baths, public entertainments, abundant food, and leisure time, they still found themselves wanting.
Their religions were many and varied. Nobody felt confident or certain about life's purpose and destination. The excellent HBO series Rome graphically shows how awful and dangerous pagan life could be - even if you were rich. The monied classes had to worry about assasination, political oppression, and the whims and insanity of the emperor. The poor were considered cursed by the gods.
Basic understanding of moral behavior wasn't held by citizens in common, so even 'civilized' life in the ancient world was frequently nasty, brutish, and short.
Christianity hadn't yet taken hold of the Roman mind by 120, and it was generally viewed as a strange cult, an offshoot of Judaism. It took almost two more centuries - well into the 300's - before it gained popularity. But in spite of ruthless and cruel persecution, Judeo-Christianity continued to grow from one end of the Empire to the other. It offered superior ideals to the ordinary citizen and slave. It saw no intrinsic difference between citizen and slave. This belief in the natural value of the individual dovetailed beautifully into the original Greco-Roman ideal if the free citizen, a creation of God.
The promise of eternal life and joy for all the faithful inspired and healed a troubled people. Honor had always been a powerful driving force in the Roman psyche, and Christianity offered ultimate honor and victory. It still does.
Our modern era is seeing the chaos of paganism once again gaining strength. Judeo-Christians and other people of great faith are under attack and retreating in many places. We really should pay attention.