I think that A is the more likely.

Does anyone remember how old Harry was when Voldemort killed his parents?

Not precisely, but he was very young. No more than a year or so old at most, I think.

I don't think that Snape hates Harry without reason, though admittedly his reason isn't a very rational one. He hates him because he's the son of James, the person who so cruelly teased him when they were schoolmates and who married the woman he (Snape) loved.