Unable to shed a file

Hello Bud,
Please be informed that it is an important system folder. All the files of the program's installed on your PC will be saved on the Program Files folder. It is not recommended to shred the folder as it may cause failure on bootup up of your PC.
Thank you.

I am trying to delete a file from my computer. It is in the "Program Files (x86) folder". When ever I try, windows says "action cannot be completed because a file or folder is open in another program". This file belongs to a program that I had just removed. So, I accessed the file in Program Files (x86) and tried to shred it with AVG. An AVG pop up window tells me that I "do not have enough access rights to shred it".

What??? What is going on with my own computer that AVG would tell me this?

Hello Bud,
Please be informed that it is an important system folder. All the files of the program's installed on your PC will be saved on the Program Files folder. It is not recommended to shred the folder as it may cause failure on bootup up of your PC.
Thank you.