I find this to be an interesting question because rather than building an imaginary world, the question is targeting what it would take to build this real world in a certain way!
Convincing a majority of people to do ANYTHING is a major task, so don't be surprised if this takes more effort than you think it will.
Changing building polices is hard. Consider places like Paris, where the streets are unfathomably difficult to follow, just because they were designed before the automobile. The acceptance of cars didn't change the city layout, so you would need to have an impact greater than that to convince historic cities to change their POV.
Accordingly, I am going to assume you are targeting the majority of single-family 1-story dwelling owners, not the majority of the world.
Most families do not have the spare finances to build a new home These underground houses do not yet exist in bulk, so each has to be built. This is going to have a strong effect on the housing market. If you did get your way, nobody would move into old homes, they'd all pick new concrete bunkers. Families with housing would have trouble selling their houses, so it would be hard to buy a new home and deal with the second mortgage.
Some areas of the world do not support such construction If you happen to live in the deserts of Arizona, you know that basements are rare, much less underground housing. The ground is not very hospitable to such excavation.
There are cultural issues to overcome. Being underground is often associated with death at some very base level. It will be harder to sell an underground house because of this built-in prejudice. Strong concrete and steel structures with steel doors would make this even more coffin like.
In all, your best course of action would be to live in one, and visibly enjoy it! I don't think you can make an argument to rapidly shift everyone from the cultural norm of building for several thousand years into a new mode overnight with just words. However, it is well recognized that people follow happy leaders in hopes of becoming happy themselves. If you build an underground home, and love it, you will naturally begin selling it as an alternative way of living just by walking around town. If you hold parties in your underground home, you get a chance to show it off. Little by little, people may turn around. Or they may not. The tricky thing about free-will is that coercing the masses is not easy. Better to be happy with what you have, and let the masses do what they like!