How To Persuade NIMBYs
One of the frustrating aspects of arguing with those who oppose new housing in their neighborhood is the typical dodge-and-weave around Econ 101 issues.  As any first-year econ student will tell you, more supply of housing will lower prices.  But many NIMBYs instead argue that more housing just drives up prices by gentrifying neighborhoods, when the exact opposite is true.
Noah Smith describes these typical arguments made by housing opponents and offers these suggestions on how to respond to them:
1. Econ 101 supply-and-demand theory is helpful in discussing these issues, but don’t rely on it exclusively. Instead, use a mix of data, simple theory, thought experiments, and references to more complex theories.
2. Always remind people that the price of an apartment is not fixed, and doesn’t come built into its walls and floors.
3. Remind NIMBYs to think about the effect of new housing on whole regions, states, and the country itself, instead of just on one city or one neighborhood. If NIMBYs say they only care about one city or neighborhood, ask them why.
4. Ask NIMBYs what they think would be the result of destroying rich people’s current residences.

5. Acknowledge that induced demand is a real thing, and think seriously about how new housing supply within a city changes the location decisions of people not currently living in that city.

6. NIMBYs care about the character of a city, so it’s good to be able to paint a positive, enticing picture of what a city would look and feel like with more development.

For a less politic take on how to advocate for housing, Seattle’s (aptly named) Dan Savage pulls no punches when it comes to what it will take to improve housing and rapid transit in our urban centers:
Housing scarcity—exacerbated by the ridiculous amount of this city zoned for single-family housing—deserves as much blame for the displacement crisis as gentrification. More. And unlike gentrification (“a once in a lifetime tectonic shift in consumer preferences”), scarcity and single-family zoning are two things we can actually do something about. Rezone huge swaths of the city. Build more units of affordable housing, borrow the social housing model discussed in the Rick Jacobus’ piece I quote from above (“Why We Must Build“), do away with parking requirements, and—yes—let developers develop. (This is the point where someone jumps into comments to point out that I live in a big house on Capitol Hill. It’s true! And my house is worth a lot of money—a lot more than what we paid for it a dozen years ago. But the value of my house is tied to its scarcity. Want to cut the value of my property in half? Great! Join me in calling for a radical rezone of all of Capitol Hill—every single block—for multi-family housing, apartment blocks and towers. That’ll show me!)

Both pieces are worth reading in full, especially for those concerned about the lack of new housing supply in our job- and transit-rich urban centers.