Increasing housing supply by 50% will increase homelessness because you have 50% more people willing to financially support it.
Neighborhoods in Tokyo have no local control over zoning, and houses are widely understood to be a depreciating asset, not an investment. So Tokyo builds enough housing and homeowners can't pull up the ladder behind them.
The homelessness rate in Tokyo is astonishingly low and decreasing: just 1600 people in a metropolis of 13.6 million. Almost everybody can afford to live somewhere, because there is enough housing for everybody to live somewhere.
You may think I'm saying that your neighborhood has to look like the Ginza area, and I'm not saying that at all. Tokyo contains some calm, beautiful, residential-focused cities such as Setagaya. (If this is confusing: a metropolis can contain a city.)
That doesn't have very much to do with whether there are enough places to live. If the places where the careers are have fewer available places to live than they have people, it doesn't matter how dedicated you are, you can still fall out the bottom of the market.
Homelessness however is more a multi-headed beast, and Japanese culture likely plays as much into a lack of people on the street as does housing availability.
At least that's what I'd be referring to if I were to make the parent's argument.