Not to mention, OVAs aren't canon, so anything that happens in them don't really have much bearing on the plot.
Left-handed people don't always do everything with their dominant hands. I myself was born a southpaw but grew up right-handed, hence why I grip my pencil weird when I write and I can beat any true righty at arm wrestling with my left hand. Handedness is kind of an anomalous thing, even of there are generalizations. Everyone has their tendencies.