Indeed you are, your missing a lot. There is countless ways you can be "left and for small government", any issue, the two are not even related whatsoever. Id like you to tell me how they are related and I will explain that. I can list every issue but that's pretty pointless, because yes I mean every single issue. You are pretty much denying the existence of every political philosophy known to man, you know why? Because everyone is essentially a libertarian or anarchist only to which degree is the variation, Statism is not based on philosophical understands, it is not based on moral principles, nor rational thought. Statism is a disease and you are infected with it. This "argument" you are having IS the state, People are not the state, its only a state of mind. People are based on moral principles, ethics, philosophy, rational thought, logic. This entity known as government is not. These are the very foundations of Libertarian and Anarchist philosophies and in statism again they do not exist. It is not based on humanity or in reality.
FYI a right libertarian or anarchist would be the minority, I seriously challenge you to find me a political philosophy that is right libertarian. There is only 4 that I can think of compared to dozens upon dozens of left libertarian or anarchist philosophies and they are pretty much in the center. Minarchism (essentially a "Republican"), Market Anarchy, Neoliberalism, & Anarcho-capitalism...We had a thread about this before and came to the conclusion that there really is no such thing as a right wing libertarian, those 4 lean right but they are technically more in the center.
Tell you what just take one week off of fox news or whatever mainstream media crap is brainwashing you and go read through that wikipedia link I gave you please for the love of god.