There are a lot of reasons why you might not be able to keep your lead arm straight as you move into the top of your backswing. Some of the reasons can be mental but there are numerous physical reasons that can cause the “breakdown” of the left arm (for right-handed golfers). Surprisingly a lot of the physical reasons have nothing to do with your elbow proper. The breakdown can start from the feet and make its way on up to the arm.
Most golfers want to get the “biggest” backswing as possible and think that getting the club shaft parallel at the top is the holy grail of creating a full turn. However, many golfers are physically unable to achieve this without creating a number of swing faults (biomechanical inefficiencies) along the way. Getting the club parallel essentially can mean nothing if you have created inefficient movement patterns that make it difficult to consistently make good contact with the ball.
I will describe a couple of physical issues that can create a “need” to bend the left arm to get the shaft parallel. The right hip joint needs to be able to move (mobility) into internal rotation in order for the trunk to make a full turn. If the right hip joint range of motion is limited in this direction (very common) it is going to be difficult for the golfer to maintain his/her address spinal posture.
The result is often standing up or losing the original spine angle. Because the hip has stopped rotating the trunk above it will need to compensate and if the golfer is trying to get to parallel the bent elbow will often create more apparent turn.
The same process can happen if the right hip is fine but the upper trunk has the inability to fully rotate to the right. The bent elbow gives the appearance of a fuller turn in the quest to get the club shaft parallel at the top.
The inability of the trunk to rotate is often due to a tight lat muscle in your back and/or soft tissue/joint restriction in the mid-back. The lat attaches to the arm and when it is tight will limit the left shoulder’s ability to move thus causing the elbow to bend and give the feeling to the golfer that they are achieving their desired parallel position.
Poor posture can affect the quality and quantity of the upper torso turn and also affects lat length. There is an epidemic of poor posture that makes it difficult to cleanly get a nice turn on the golf ball.
That leads us on up to the left shoulder. The back side of the left shoulder needs good mobility in order to create a solid turn and to keep the elbow straight. There are upper arm muscles that span the distance from above the shoulder joint, around the back and to below the elbow joint. Thus the back is connected to the shoulder is connected to the elbow and restriction or tightness in one can affect the others. Again, if the body parts above the shoulder and elbow are not moving properly the breakdown of the left elbow can be imminent in the quest for parallel.
The bottom line is it probably does not make sense for most amateur golfers to strive to achieve the parallel club shaft position at the top of their backswing if it means allowing the elbow to bend. It does make sense however to make sure all of your body parts are moving optimally to create the leverage that the straight left arm can afford. To find out if you have some mobility issues than can lead to biomechanical swing inefficiencies, consider a TPI physical assessment and a custom exercise program to address your limitations.