When you click the Button1, at first page load event fires, so your dropdown list will get reset by fetching its values from the database.
Try to put a checking, whether its postback or not.
protected void Page_Load(object sender, EventArgs e)
{
if (!IsPostBack)
{
SqlConnection con = new SqlConnection(ConfigurationManager .ConnectionStrings["cn"].ConnectionString);
string com = "select * from abouts";
SqlDataAdapter adpt = new SqlDataAdapter(com, con);
DataTable dt = new DataTable();
adpt.Fill(dt);
DropDownList1.DataSource = dt;
DropDownList1.DataBind();
DropDownList1.DataTextField = "title";
DropDownList1.DataValueField = "id";
DropDownList1.DataBind();
}
}