Here are some alternatives for you,
What you can do is Remove me.close() OR
go to solution explorer → My Project → on application tab.
you will notice at the bottom: shutdown mode.
change it to "when last from closing". (check the attachment)
the reason is:
When you are using me.close on the form 1
and at the time by default the application setting is as
shutdown mode: When startup form closes.
so When your First form is going to close at the time all else form which are linked with it will closed. So for your situation you can not close it. (you can hide it)
But on the Form 2 Closes you should also need to close first form.
On form2 => formclosing event will be:
but I will prefered you to change the setting. as shown in previous details.
Reason: You can close any form, but the application will not end untill the last form is opened.