How to add a self-defined MouseMotionListener to a JPanel?

In the code in your question, you are adding a JPanel to a JPanel since MouseMotionEvents is a JPanel (since it extends class JPanel). The default layout manager for JPanel is FlowLayout which tries to display its contained components at their preferred size. So when you run your GUI, you cannot really see where MouseMotionEvents appears. You can add a border to it by adding the following (in the constructor of class MouseMotionEvents)

setBorder(javax.swing.BorderFactory.createLineBorder(java.awt.Color.red));

Now when you run the GUI, it looks like this

This is because a JPanel has zero (preferred) size because its size is determined by the components that it contains but in your code MouseMotionEvents contains no components. You can fix this by explicitly setting a preferred size. This is how it looks after setting an appropriate preferred size.

Now you can drag the mouse inside the red border and rectangles will be drawn.

Also, you should override method paintComponent and not method paint. Refer to Performing Custom Painting.

Here is the code.

import java.awt.Color;
import java.awt.Dimension;
import java.awt.Graphics;
import java.awt.Point;
import java.awt.event.MouseEvent;
import java.awt.event.MouseListener;
import java.awt.event.MouseMotionListener;

import javax.swing.BorderFactory;
import javax.swing.JFrame;
import javax.swing.JPanel;

public class MouseMotionEvents extends JPanel implements MouseListener, MouseMotionListener {
    Point p;
    Point r;

    public MouseMotionEvents() {
        addMouseListener(this);
        addMouseMotionListener(this);
        setBorder(BorderFactory.createLineBorder(Color.red));
        setPreferredSize(new Dimension(300, 300));
    }

    public void mouseClicked(MouseEvent me) {
        // p = me.getPoint();
        // repaint();
    }

    public void mouseEntered(MouseEvent me) {
    }

    public void mouseExited(MouseEvent me) {
    }

    public void mousePressed(MouseEvent me) {
        System.out.println("mousePressed");
        p = me.getPoint();
        // repaint();
    }

    public void mouseReleased(MouseEvent me) {
        System.out.println("mouseReleased");
        r = me.getPoint();
        repaint();
    }

    public void mouseDragged(MouseEvent me) {
        r = me.getPoint();
        repaint();
    }

    public void mouseMoved(MouseEvent me) {
    }

    protected void paintComponent(Graphics g) {
        super.paintComponent(g);
        if (p != null && r != null) {
            Dimension d = getSize();
            int xc = d.width / 2;
            int yc = d.height / 2;
            if (p.x - r.x > 0 && p.y - r.y > 0) {
                g.drawRect(p.x, p.y, (p.x - r.x), (p.y - r.y));
            }
            if (p.x - r.x > 0 && p.y - r.y < 0) {
                g.drawRect(p.x, p.y, (p.x - r.x), (-p.y + r.y));
            }
            if (p.x - r.x < 0 && p.y - r.y > 0) {
                g.drawRect(p.x, p.y, (-p.x + r.x), (p.y - r.y));
            }
            if (p.x - r.x < 0 && p.y - r.y < 0) {
                g.drawRect(p.x, p.y, (-p.x + r.x), (-p.y + r.y));
            }
        }
    }

    public static void main(String[] args) {
        JFrame aWindow = new JFrame();
        aWindow.setBounds(600, 600, 600, 600);
        aWindow.setDefaultCloseOperation(JFrame.EXIT_ON_CLOSE);
        JPanel content = new JPanel();
        content.add(new MouseMotionEvents());
        aWindow.add(content);
        
        aWindow.setVisible(true);
    }
}

Note that x and y are public members of class Point so no need to use methods getX and getY and therefore no need for casting.

When you added MouseMotionEvents directly to the JFrame you were adding MouseMotionEvents to a JPanel with BorderLayout and you were adding it to the CENTER. Since you gave your JFrame and explicit size, the BorderLayout made sure that the size of MouseMotionEvents took up as much space as possible in the JFrame. Hence MouseMotionEvents was large enough that you could drag the mouse inside it.

To add a MouseMotionListener to a JPanel, you have to use

myPanel.setMouseMotionListener ( myMouseListener );

and call that directly on your panel, as you did in the mouseMotionEvents class. Tht's why it's working, when you add this directly to your JFrame.

After fixing your code I got this, which should work perfectly fine. I splitted it in two classes, one main class with JFrame and one for the JPanel (content).

Main class:

public class MouseMotionListenerTest {
    public static void main ( String[] args ) {
        JFrame aWindow = new JFrame();
        aWindow.setBounds( 600, 600, 600, 600 );
        aWindow.setDefaultCloseOperation( JFrame.EXIT_ON_CLOSE );

        ContentPanel content = new ContentPanel();
        aWindow.add( content );

        aWindow.setVisible( true );
    }
}

Panel class:

public class ContentPanel extends JPanel {
    private Point p;
    private Point r;

    public ContentPanel () {
        MouseMotionEvents mme = new MouseMotionEvents();
        addMouseListener( mme );
        addMouseMotionListener( mme );
    }

    public void paint ( Graphics g ) {
        if ( p != null && r != null ) {
            Dimension d = getSize();
            int xc = d.width / 2;
            int yc = d.height / 2;
            if ( p.getX() - r.getX() > 0 && p.getY() - r.getY() > 0 ) {
                g.drawRect( ( int ) p.getX(), ( int ) p.getY(), ( int ) ( p.getX() - r.getX() ), ( int ) ( p.getY() - r.getY() ) );
            }
            if ( p.getX() - r.getX() > 0 && p.getY() - r.getY() < 0 ) {
                g.drawRect( ( int ) p.getX(), ( int ) p.getY(), ( int ) ( p.getX() - r.getX() ), ( int ) ( -p.getY() + r.getY() ) );
            }
            if ( p.getX() - r.getX() < 0 && p.getY() - r.getY() > 0 ) {
                g.drawRect( ( int ) p.getX(), ( int ) p.getY(), ( int ) ( -p.getX() + r.getX() ), ( int ) ( p.getY() - r.getY() ) );
            }
            if ( p.getX() - r.getX() < 0 && p.getY() - r.getY() < 0 ) {
                g.drawRect( ( int ) p.getX(), ( int ) p.getY(), ( int ) ( -p.getX() + r.getX() ), ( int ) ( -p.getY() + r.getY() ) );
            }
        }
    }

    private class MouseMotionEvents extends MouseAdapter {
        public void mouseClicked ( MouseEvent me ) {
            // p = me.getPoint();
            // repaint();
        }

        public void mousePressed ( MouseEvent me ) {
            p = me.getPoint();
            // repaint();
        }

        public void mouseReleased ( MouseEvent me ) {
            r = me.getPoint();
            repaint();
        }

        public void mouseDragged ( MouseEvent me ) {
            r = me.getPoint();
            repaint();
        }
    }
}