Two truth(ish)s and a few lies.
Yes, we have an AFFORDABLE housing shortage. We are absolutely not keeping pace with building new housing... but specifically affordable/subsidized housing. Unregulated temporary rentals (VRBO/AirBnB) have also decreased the inventory dramatically, exasperating the problem.
** no human is illegal **
If you think migrants, refugees and asylum seekers are taking up $3,000 one bedroom homes... i have a border wall to sell you.
The houseless and unstable housing crisis is also a product of the privatization of our health care industry and the deconstruction of our mental health care systems (thanks Ronald!), the stagnation of minimum wage (thanks republicans), the climate crisis (thanks corporations and anti-science dwerps!) and the exportation of manufacturing (we all need to eat this one... but thanks Biden and the unions for working to bring it home again.)