I like P45cal's method, with one little addition
Private Sub Workbook_SheetChange(ByVal Sh As Object, ByVal Target As Range)
If Target.Column <> 1 Or Target.Cells.Count > 1 Or Target = "" Then Exit Sub
Application.EnableEvents = False 'needed to stop your original error.
'Target.Row does not indicate which sheet. Target.Offset does
'Use
'Sh.Rows(Target.Row + 1).EntireRow.Insert
'Or
Target.Offset(1).EntireRow.Insert
Application.EnableEvents = True 'reinstate.
End Sub
Private Sub Workbook_SheetChange(ByVal Sh As Object, ByVal Target As Range)
If Target.Column > 1 Or Target.Cells.Count > 1 Or Target = "" Then Exit Sub
Application.EnableEvents = False 'needed to stop your original error.
Target.Offset(1).EntireRow.Insert
Application.EnableEvents = True 'reinstate.
End Sub