Why is my button placed like that?

The problem is that the width variable is not set until the size() method is executed in setup()

Change your code to

int buttonSize = 260;
int buttonY = 500; 
int button2X; 

and in setup

void setup(){
    size(480, 320); // use your own width and height
    button2X = width/2-(buttonSize/2); 
    // rest of your setup code
}
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