I think it's just joking on households often having one wobbly or half broken chair.

It's not a safe chair.

I thought about this later, and now I think it's this: The host says to the guest "have a seat anywhere" only to come in and find the guest has selected the worst, most obviously dangerous seat.

My childhood included my mother owning furniture that was decorative, but that we were not allowed to use.

Some was just because children are messy, but some was because the furniture was just old and couldn't handle abuse from people sitting too hard or putting stress on unexpected angles.

That's what this makes me think of

I'm assuming that that's for the husband due to the clothing being similar to older people and most old jokes being akin to "I hate my husband/wife".