Immigration Law -- I don't get it

Let's start by understanding what our current immigration law states.  As a country, we have always been a refuge for the weak --"Give me your tired, your poor, your huddled masses yearning to breathe free..." so we have always been a country that welcomed newcomers.  This is a foundational strength of the United States of America that we are made up of millions of dissimilar people who share fundamental beliefs (let's just assume that we still share fundamental beliefs).

In any case, part of the sharing is that each person who comes to this country must abide by a certain set of rules that we call laws.  Some of those are things like you should pay taxes, others are things like you can't murder your enemy, and still others are things like you have to seek approval to be accepted into the country.  Once you are accepted into the country, we welcome you with open arms and give you access to freedoms and a lifestyle unparalled in this world.  You do, however, have to be accepted.  We can argue whether we should accept all people or if we should be selective, but for now the law is that we have to accept you.  In fact, here is a quick quote on the law:

"Unlawful Entry

In addition to facilitating the lawful admission of both immigrants and nonimmigrants, U.S. policy addresses the issue of unauthorized aliens in the United States. According to the Census Bureau and the former Immigration and Naturalization Service, about 7 million unauthorized aliens were in the United States in 2000. Other researchers have estimated that number at roughly 10 million in early 2004. Although such estimates convey the population of unauthorized aliens living in the United States in a given year, the other statistics presented in this paper represent annual inflows of people into the United States, unless otherwise indicated. Aliens found to be in violation of U.S. immigration laws may be removed from the country through a formal process (which can include penalties such as fines, imprisonment, or prohibition against future entry) or may be offered the chance to depart voluntarily (which does not preclude future entry). In 2004, about 203,000 people were formally removed, and about 1 million others departed voluntarily (some people may have done so more than once). Of the 203,000 formal removals, 42,000 unauthorized aliens were subject to expedited removals, a process designed to speed up the removal of aliens seeking to enter the country illegally."

This was taken from http://www.cbo.gov/ftpdocs/70xx/doc7051/02-28-Immigration.pdf

So what is all of the noise about the Arizona law that is designed to enforce this law.  Let's look at how ridiculous the arguments are against this law.

As a person, I have to prove who I am all of the time.  I have to prove who I am when I go to the doctor's office, when I go on an airplane, and many other times.  Here is a picture someone put together that highlights how often we, as American citizens, have to prove who we are: