How can I invite persons to my home without a hub ?

I also did this with my wife and kids before the update, and now after the update we suddenly need to have a hub, why do I need it now, when I did not need it before?

Nice of Apple to warn us before making this new upgrade and requirement. NOT! I upgrade to the new core tech only to then discover I couldn't share without buying new/additional equipment. To be honest I would expect a lot more from Apple.

So now the question is "how to downgrade or back grade to the previous tech so I can make my existing equipment work and share with the other previous users?"

Did you Upgrade to the new Home architecture?

Any device that is connected to an upgraded home and not running the latest software will lose access to the home until the device is updated. This includes people that you invite to control your home.

Once you’ve upgraded to this, any devices not running the latest software can’t use the home app (on that device) or receive invites.

As per your title “without a Hub”. You need to have an Apple TV or HomePod to act as the hub to set up Homekit in the Home App.

HomeKit requires an Apple device home hub, even with other bridges.

Else you have no HomeKit home to invite people to.

Delete any pending invitations

You can only invite people when you're home and connected to your home Wi-Fi network. 

Make sure that you and the people you invite are signed in to iCloud on iPhone, iPad, or Mac. In iCloud settings, turn on Home.

See: Share control of your home - Apple Support