The screenshot in your post is showing a Web AppBuilder for ArcGIS application - are you using this app in Portal for ArcGIS?
> why is there is no invert selection / switch selection option available
To be clear, are you referring to the Attribute Table widget - shown at the bottom of the app?
Attribute Table widget—Web AppBuilder for ArcGIS | ArcGIS
Switch selection is not part of the functionality, but this is a good enhancement request. Please post your enhancement on the ArcGIS Ideas site for Web AppBuilder.
Hope this helps,