This question has been asked, and answered so often already. Yet, I'm going to answer it again. I'm going to pretend that the previous times that this question has been asked, and answered in so many media outlets just got missed by you.
1) It's curious that all the political, and social leaders, who say that walls don't work all live behind walls. President Obama had dozens of people who were dedicated to his safety, and for some reason they wanted a higher fence to help them.
But let's start at the beginning shall we? Do you lock your doors at night? Do you imagine that these doors will prevent a determined madman from getting into your house and rampaging through your family? Is it racist for you to lock your doors?
The obvious answer is yes you lock your doors, and no it will not stop someone from kicking your door in or smashing it in with a battering ram or sledgehammer. So why do we do it? Partly it is a psychological barrier. We feel better knowing our doors are locked. Partly that psychological barrier is actually physical. The smashing of the door will make noise, and alert us that someone is now inside.
We lock our cars for the same reason. Again, it won't stop the determined individual, but it will slow them down.
How about the individual looking for the easy opportunity? They will be deterred from taking our stuff from the car by the doors being locked and the windows up. They will go on looking for an easier way. The thief looking to just pop in and snag something from a house if it is easy will not kick the door in if it can be avoided. They'll move along, afraid of finding that the act of kicking the door in will alert the occupants, and they might be armed with a gun or whatever.
Walls and fences are literally chapter one page one of any security manual. The purpose according to the Army, of any obstacle is to delay or deter the enemy. Delay, or deter. You notice it is not to stop them cold, but to delay, or deter. To force the individuals to expend more effort, and time, to get through, over, or around the obstacle.
2) Nobody is suggesting that the wall is the answer in and of itself.
Just as President Obama's security was not left up to the fence around the White House, no one is suggesting that once we build the wall we can fire all the Border Patrol officers.
The wall is part of a comprehensive security package. It must be backed up by over watch, that is to say someone has to keep an eye on it. The eye may be electronic, or physical. But someone must be using the wall to identify when, and where, someone tries to gain entry. Just as you would not ignore the pounding as someone smashed into your door with a hammer. You would move to intercept the individual before they got very far into your house.
Safe's like you would use to keep Jewlery or firearms in are rated in how many minutes the individual breaking in will be delayed. From a handful, to several hours, the delay is calculated based upon the tools and experience needed. You mentioned that the people seeking to enter can climb over, or tunnel under.
Yes, they can. However, that is where the delay factor comes in. If it takes them ten minutes to climb over, then you have delayed them ten minutes. Ten minutes to get someone started on the way to intercept the individuals coming over. You can use that time to get an accurate count. Five or fifteen makes a difference. If you are looking for fifteen, and you find five, you know that there are ten left to keep looking for.
Tunneling under takes even longer. Days minimum, weeks probably, and possibly months. Better yet, Tunneling makes noise that can be heard with ground listening devices. Tunneling is also dangerous, as the tunnel can and does collapse trapping the people inside. The wall raises the stakes, making crossing the border a potentially fatal endeavor.
This was apparent even to the Chinese who built the Great Wall. There were towers where guards were stationed to keep an eye on the wall.
2) Immigration. Speaking for myself, I am not opposed to greater immigration numbers. But is that racist? Let's see shall we?
Back to the analogy of your house. When someone knocks on your door, do you open it wide automatically? Normally, people open the door wide when the person is identified. Someone known to you will find the door opened wide, welcoming them into your home. A person who isn't known to you will be faced with questions. Who are you, what do you want?
Is it racist for you to ask those questions? Or is it a common sense precaution that everyone takes at their door? Why is it racist to do the same to our collective door, the border?
There is much more that can be said, but I am going to assume that either you will ignore this, or decide that these common sense and logical statements are motivated by whatever hatred you think is in my heart.