Perfectly put.No - it’s stop punishing the children of the worse off who are in no way responsible for the deck of cards being stacked against them and to stop rewarding the children of the better off who are in no way responsible for the deck of cards being stacked for them.
It’s a pretty simple aspiration (albeit impossible to fully attain in reality) - every person is born with as equal an opportunity as possible and makes their own success in life. Their success or failure is not directly linked to factors outside their control (i.e. the success or failure of their parents) . If you agree with that statement - I see anything other than wanting higher inheritance tax and lower income tax as contradictory.