I have been shopping around for a while looking for a used car. Most of the time I have requested to test drive the vehicle and the owners insist that they drive it. I mean, how can you buy a used car without test driving it. Has anyone too encoutered this problem and do you think it is fair....anyway just very annoyed with these people....

I've had that problem before. Its fair enough if they want to be in the car while you take it for a test drive but if they won't even let you drive it, how can you decide if you like it enough to buy it. If they won't let you drive it... easy fix... walk away. There is no reason why you have to buy a particular car. If they really want to sell the car, it won't take them long to let you have a drive if they see you walking away.
Good luck with the next one.

I would never buy a used car that someone won't let me drive, unless in exceptional circumstances like at an auction or if they're uninsured.

Really, its hard to test a car to see if its any good if you don't get to try its primary function - driving. I'd be looking elsewhere if I couldn't test drive.