Two major reasons and a slew of minor ones.

1. Both the jet stream and prevailing winds in Canada blow from the west. In BC, that means warm moisture laden air blowing off the relatively warm Pacific.

2. The Cascades and Rockies act to block the worst of the Arctic outflows. The cold air gets channeled down the western slopes of the Rockies before the jet stream takes it east.

Canada's east coast does benefit from the moderating effect of the ocean but with no blocking mountain range, prevailing winds blowing from the west, and the really warm Gulf Stream current well offshore, there is only so much moderating the Atlantic can do.

Now in Western Europe, the Gulf Stream provides a BC like climate at the same latitude.

I've lived in Vancouver but now live in the southern interior. As much as the west coast can grow palms, I think they look totally out of place. Give me a beautiful Arbutus tree any day.