What are the two best explanations for why the US continues to struggle with protecting its borders?
The two best explanations for this are A) the amount of border that we have to protect and B) the fact that we are free country.
The borders of the United States are tremendously long and therefore very hard to protect. People can walk across the border relatively easily in many places. They can enter by boat along our long coastlines. This is not a small country that can be easily shut off from the rest of the world.
Our country is based on individual freedoms and limited government. This means that it is hard for the government to do some of the things that might be necessary in order to secure our borders. The government cannot easily force businesses to take responsibility for determining whether the people they are hiring are in the country legally. It cannot easily require landlords to check on the immigration status of their renters. It would be very hard to get the people to accept having the government randomly checking for people's immigration status on the street. Because we are so attuned to the idea of civil liberties, it is even harder to protect our borders and keep illegal immigrants out.