However, this issue can be solved with a little clarification and a few minutes practicing in front of a mirror. As having acknowledged that, it is ideal (simplest and most efficient) to keep the left arm extended in the backswing and downswing through the impact zone. But as long as the left arm returns to straight before impact it is not crucial to keep it perfectly straight in the backswing.
Even though the preceding paragraph is true, most healthy golfers with normal ranges of motion should still easily be able to keep their left arm fairly straight throughout the backswing. Why then do so many people have trouble with it? There are a couple typical reasons: substantial movement of the arms separately from the torso and/or overswinging.
Most people that complain of this problem try to move their arms and hands farther around than their torso has turned. The left arm should not continue to wrap around the upper torso or neck once the shoulders have stopped rotating; it simply lifts up a little bit, if anything. This means that your arms and hands are still pretty much extending in the same direction as your chest is facing at the top of the backswing, not wrapped around your neck or behind your back.
Now, keeping your eyes and face toward the mirror, turn your shoulders so that they are as close to 90 degrees, or your full backswing torso turn, as possible. Your arms simply turn with your torso. As you look in the mirror your left arm should still be parallel to the ground and it should still be very easy at this point to keep it straight.
From this position if we simply included a forward tilt of the spine toward the mirror, as you would normally have in your address position, and optionally a slight further lifting of the arms, we'd pretty much have a standard-issue top-of-backswing position.
In addition, limited flexibility is a problem to some people. You can get a golf professional in person to have that assessed. This is fairly rare and can easily be dealt with by taking a shorter backswing. It is also a good way to work on your flexibility.
If you are one of those who in the proble of keepping left arm straight, take a look at this article and follow these small tips to have a try. After practice, you will find yourself less worried wabout this matter.