I don't really see this a feminist issue.
I'm a landlord. I own 2 flats neither of which are suitable for families, although one I did let to a family as I was confident they would pay the rent.
I can't , because my house insurers won't allow it, take any tenant who is not a student or in full time employment. Neither of the companies who insure my flats will insure them if the tenants are on housing benefit. That might seen unfair but private landlords are not providers of social housing.
Like most landlords I specify no pets and no smoking. That's tough on people who want to smoke and/ or have cats. I have cats; one of them pees in my house. My choice, I can live with that. One of my tenants, in breach of her tenancy agreement, had 2 cats in a flat which had no direct access to a garden. They peed
all over the place and I had to pay a lot of money to have the original Victorian doors which her cats scratched sanded and varnished, and for professional cleaning of furniture, which she refused to pay for. Had she agreed to make good the damage caused by her pets it would have been fine.
This landlord seems a pretty vile person as he is setting arbitrary rules and apparently not abiding by his obligations as a landlord to maintain his property.
Most landlords will assess tenants on their individual ability to pay rent and whether they will not cause damage to the property, subject to the constraints imposed by insurers which , aside from the large corporate portfolio landlords, most landlords can't ignore.
We have a problem, a major problem, with housing in the UK.
The Scottish Government sets far higher standards which landlords in Scotland have to meet than in England and Wales to the extent that the first flat I bought for me to live in would now not meet acceptable standards to let it out.
Due to the, in one way brilliant piece of, social engineering of Thatcher in allowing the purchase of council houses we have this problem.
Oh I as a good little champagne socialist was hugely against this ; never having lived in a house which wasn't owned by either my family or me. Her policy allowed social mobility on a level which had almost never been seen before.
The problem is that those houses were not replaced and publicly owned housing stock is now subject to ghettosiation.
This man is horrible. However setting that aside we need a far greater building programme of publicly owned housing.