MouseUp rightclick works where MouseClick doesn't

Question

I'm making a GUI in C#, and am trying to handle right clicks. I started with adding a Click event to each button, which didn't work, and I found this question, which led me to use MouseClick.

private void InitializeComponent() {
    ...
    var b = new Button();
    b.Dock = DockStyle.Fill;
    ...
    b.MouseClick += OnClick;
    b.text = "";
    ...
}

private void OnClick(object sender, MouseEventArgs e) {
    if (e.Button == MouseButtons.Right)
        ((Button)sender).Text = "right ";
    ((Button)sender).Text += "clicked";
}

Now, when I left click it works, but right click is still not recognized. However, b.MouseUp += OnClick works correctly.

Does anyone know why that is?