Sure, I'll give it a try.

Pro-housing, in the strongest flavor I think can reasonably be sustained: shelter is one of the most fundamental human needs. We need shelter from the environment and shelter from those who would harm us or take our things. It is our responsibility as members of a just society to help our members meet critical needs, including the need for shelter. Our standard way of providing shelter is for people to have a home: a place that is safe, comfortable, and where they can organize their own affairs without the constant stress of interference. Having a home greatly enables people to learn, develop, and take on more responsibilities themselves, thus strengthening the effectiveness of society as a whole. We therefore should ensure that there is adequate housing--at least at some minimal level--for anyone who wishes it, regardless of their desire to pay. Just as public education is a long-term investment with enormous dividends, so too should public housing be viewed as a long-term investment with sizable dividends. Because it is a long-term investment, the responsible parties must be those who can afford long-term investments: governments, banks, and the like. Likewise, because the benefits accrue to society as a whole and the financial burden is great, the investment should come from society as a whole (tax revenues).

Anti-housing, in the strongest flavor I think can be reasonably sustained: every member of society has a fundamental responsibility to take care of and provide for themselves to the extent possible. Although there are occasionally exceptions due to disability and age, in practice almost every adult can engage in productive work earning a sufficient salary to afford basic shelter. If they choose to sacrifice shelter in pursuit of other things, it is their responsibility not to burden the rest of us with it--so not only should we not reward their choice by burdening ourselves with providing them housing, they also need to ensure that their lack of housing does not cause a public nuisance. In those cases where the individual somehow cannot find gainful employment, the problem is with them, not with the lack of free housing, and our responsibility, if any, is to help overcome the problem that is preventing them from being willing or able to contribute as a productive member of society.

So, that's my shot at opening statements. I think it would be a lot harder to make progress working from rights instead of responsibilities. In particular, in my fantasy above, both sides have to recognize that everyone has responsibilities to everyone else, but the emphasis is different (and there is a disagreement over some factual matters--but this could be resolved with evidence).