I would suggest that you do that, CodeToad.
The Head of Government is typically the ‘leader’ of a country (I’m loath to say ‘always’, but any exceptions would be few and far between).
The Head of Government makes Federal (or ‘national’, if you will) government appointments, and wields all or essentially all Executive authority.
One sees this in most if not all Parliamentary systems - The PM is Head of Government is considered the ‘leader’ of the country, and the President, usually chosen from within the majority party, is a mostly ceremonial office. One hears very little from the President, and I’d venture to guess that few outside the country even know or care what the President’s name is - think France, Germany, or even Israel. In the European monarchies, no one would say that the monarch, as Head of State only, is the ‘leader’ of the country.
The US is one of the few large countries that combine the positions of Head of State with Head of Government (only Brasil comes to mind). I’ll surmise that that is the main source of your confusion, and that you know how rare combining the positions is. I’ve never seen anyone claim that the highest-ranking member of a legislative body is the leader of a country.
I find B Hussein’s being called our ‘leader’ as distasteful as you probably do, but there’s no need to make shiite up about the Speaker position to show your distaste.
“Head of Government”
The US is a unique country in that we have equal branches of government, not a single leading entity as you think there is. We have no “Head of Government” as you claim.
The President is the head of the Executive branch, not of “The government”, as you claim.
The Congress is the Legislative branch, with equal standing as the Executive branch.
The Judicial branch is another equal branch, not overshadowed by the President or Congress.
The Congress has the right to call/invite whomever they want without the President saying squat about it. They have equal standing and the President is not their leader.
Your civics knowledge is typical distorted public school education. They haven’t taught proper civics in decades.