You've never heard someone say "under communism, private property isn't allowed, so you have to share a toothbrush?" I heard that nonsense all the time growing up.

Your toothbrush and clothing are personal property. The family farm is private property.

The full term is private property over the means of production.

The family farm would only fall into that category if youre employing others for profit.

If you're working yourself on it, there is no real social function to it.