Telephone companies have the ability to block these numbers - just do it

Got a call.  "Hello, You have won Air Miles reward miles"  Pressed "1", got into an argument with the people because they wouldn't release which company they represented. He asked for my information, but when I aske dto speak to his manager, he told me flat out "no".  I asked to be removed off and talk to his manager, and then he said I would be removed and hung up on me.

1)  How the heck are you going to remove me if you don't know who I am?
2)  This is not a normal North American legitimate practice because no legitimate company would hang up on you unless you were swearing/threatening on the phone.

I hate these companies and will continue to press "1" until I figure out who the heck I'm calling and how they got my info.

I wish the call type below had "Suspected SCAM".

Michael

Scam...airmiles...this is getting pathetic.  3 times a day from different numbers between the mobile and home phone...really?!?

Just like everyone else, called and said I won 100,000 Airmiles Points, Press 1 to continue.

Same... Air Miles scam, recorded voice. ?Hung up.

Just wanna know what the airmile scam is and how it works so we can recognize and ignore it?