user and password have been allocated as single element arrays. Arrays are immutable and cannot be appended to, so you cannot do this:
public string[] user = { "username" };
public string[] password = { "password" };
//...
user.Append(textBox1.Text);
password.Append(textBox2.Text);
But you could reallocate the user and password arrays with something like this:
public string[] user = { "username" };
public string[] password = { "password" };
//...
user = new[] { user[0], textBox1.Text };
password = new[] { password[0], textBox2.Text };
This is rather clumsy, though. You would probably be better off defining user and password as List<String>, i.e.:
public List<string> user = new List<string>() { "username" };
public List<string> password = new List<string>() { "password" };
//...
user.Add(textBox1.Text);
password.Add(textBox2.Text);
string[] user = { textBox1.Text };but why?userandpasswordvariables just strings as it doesn't seem like you are actually using an array, just single values. Then you can just assign directly from theTextproperty.