Why the modest inflation?

[Travlyr]

Let's look at a simple example of how new money usually enters the economy.

Depositors deposit THEIR money with banks > banks PAY Treasury to buy securities > now Fed pays newly created money to banks for the securities.

That is not money PONII. That is currency. There is a great deal of difference between the two.

[Zippyjuan]

Assets - Liabilities, Zippy. You're again forgetting the liabilities. If I take out $1 trillion in liabilities its very easy to own $1 trillion in securities.

Another way to look at it is this: If the Fed wanted to sell all of its assets to contract the monetary base back to 0, could it do it?

No, they could not...

Why couldn't they sell them?

You are right it would not bring the monetary base to zero. What is in the monetary base:
http://research.stlouisfed.org/fred2/series/BASE/

The Adjusted Monetary Base is the sum of currency (including coin) in circulation outside Federal Reserve Banks and the U.S. Treasury, plus deposits held by depository institutions at Federal Reserve Banks. These data are adjusted for the effects of changes in statutory reserve requirements on the quantity of base money held by depositories.