I'm not sure what else to tell you other than what you are saying is factually wrong.
Federal aid to states is counted in federal expenditures. This is in fact one of the reasons why total spending is lower than the sum of the 'federal' and 'state and local' tabs. It is not counted twice. The 'total' is combining federal, state, and local expenditures. State and local expenditures primarily come from state property, income, and sales taxes. None of this revenue is federally generated, and states do not contribute to federal expenditures from their budgets (generally).
I seriously don't understand what you aren't getting about this. Total spending is not total federal spending, it is total spending at all levels of government. That's why there are different tabs for each type of expenditure.
Feel free to admit you were wrong at any time.