[Aguila Blanca]

It comes from an understanding of what the words "admitted to" mean.

When you first arrived in the United States, you "entered" under the authority of a non-immigrant visa. For the duration of that visa, while you were in the U.S. you were present under the authority of that visa. Thus, you were "admitted to" the U.S. by the non-immigrant visa.

That non-immigrant visa no longer exists. Although you may not have physically left the United States, your authority to be here is now a green card. Assuming that you didn't depart under the non-immigrant visa and then re-enter under the green card, your status changed by the stroke of a pen. The result is that your authorization to be in the U.S. now derives from your green card. Thus, you have now been "admitted to" the U.S. by the green card.

You are confusing "entered" with "admitted to."