I think we are in agreement for most of the things. I am glad to see we agree that the money from the Govt is not "given" to the people. This was the point of my first comment.
I just want to disabuse you from this idea you seem to hold that the money I received is from "other people".
It is not. It is from the Government. Sure it was taken from all of society via taxes, but once it is taken it is no longer yours or mine to determine what to do with it.
There is no point in trying to argue who-paid-for-what in this redistribution made by the Government. If there were a choice for tax payers to say where they want their taxes to go, sure let's go and talk about "Who is paying for my wife's Elterngeld". But there is no such rational and efficient resource allocation method in any Big Welfare State, is there? There is no way to pull apart who is "me and my family" and who is "the rest of society", is there?
There is just - like you said - one big redistribution of wealth driven by bureaucrats who are (allegedly) working in the best interests of the people. What is good for the goose is good for the gander.