I think you would have to use a control object of some type, where you would
select the row for the insert to execute on and then click the control which
would initiate the insertion based on the selection.  To use double click on
a point on the worksheet would require deactivating the current double click
event which allows edit access to the active cell.

One of the following will do it. Note that it inserts a row under the row
that is double clicked.

Private Sub Worksheet_BeforeDoubleClick _
   (ByVal Target As Range, Cancel As Boolean)

   Cancel = True   'Cancel Edit mode started by double click
   
   ActiveCell.Offset(1, 0).EntireRow.Insert Shift:=xlDown
   
End Sub

The following is similar but will only run if you double click column A.

Private Sub Worksheet_BeforeDoubleClick _
   (ByVal Target As Range, Cancel As Boolean)
   
   Cancel = True   'Cancel Edit mode started by double click
   
   If Target.Column = 1 Then
       ActiveCell.Offset(1, 0).EntireRow.Insert Shift:=xlDown
   End If

End Sub

Forgot to say right click on the worksheet name tab and select View Code and
insert one of the macros into the editor and then close the editor (X in red
background top right of screen)