Housing is expensive in BC because rents are high, with speculation on top of that. Rents are high because getting new housing approved always requires rezoning, which is slow and difficult. In Vancouver, each project requires time-consuming negotiations with city staff, which then need to be ratified by city council after a public hearing with vocal opposition from the immediate neighbours ("we're full").
Market Urbanism describes the general problem:
Many U.S. cities force every development proposal to go through a long and costly discretionary review process. This is often done by making land-use regulations so restrictive that any development must pursue a discretionary action like a rezoning or a special permit. In practice, this submits all proposed development to months of negotiating and public review, in which locals can shout a project down to their preferred size (which is often a vacant lot) or extract large concessions from the developer.
The city of Vancouver is trying to approve more rental housing, with a goal of 20,000 additional housing units over 10 years, but it's not easy to vote in favour of a project after hearing from its opponents. Each housing project reduces rents everywhere by a bit - a significant benefit for the region as a whole - but it's the immediate neighbours who bear the cost and inconvenience of living next to a construction zone. (It's a "collective action problem.")
If local governments can't figure out how to approve more housing, I expect the province will need to step in, in the same way that West Coast states in the US are overriding local NIMBYism. The provincial government may be in a better position to resolve the conflict, since the benefits of more housing are region-wide.
A number of signals in recent months indicate that Attorney General and Housing Minister David Eby—a lawyer and one-time civil liberties advocate—is ready to adopt some measures similar to the wave of new pro-housing laws that various American states have introduced in recent years. “We’re looking at absolutely anything to address the affordable-housing crises,” Minister Eby notes. “We are looking at American jurisdictions.”