Let us not forget that, as with many things, there are multiple causes. Now consider the Roman empire as a diverse group of ethnicities and ideas without the instant communication structures we have today. You're bound to have varied reasons to persecute.
I've seen nothing here that is out of the ordinary for why Romans persecutd Christians except where martyrs deterred further Christians (it often inspired further Christians from admittedly biased contemporary accounts).
Nor is that uncommon. Often harsh oppression or punishment meant to deter simply strengthens the resolve of the group. Persecution tends to have two effects. Some will desire to distance themselves from the group to be accepted by the main stream. Others will band together for mutual support, strengthening the bonds and determination of the group as they are further isolated.
Christian martyrs would have inspired both responses, as did Jewish persecution, persecution of the Romny etc.
