The straight leg raise is one of the FMS movement screen tests, which many people can't perform adequately because of hamstring mobility restrictions.
As you'll see in the video, that limitation isn't always flexibility, it's often core control or stability that they're missing. In other words their nervous system is limiting their mobility because they have "forgotten" how to engage their core musculature.
This core engagement is meant to be an unconscious reflexive response to movement, not a strong conscious muscle contraction.
This is just another demonstration of how the body is a unit, controlled by the Central Governor (Central Nervous System), which will limit our ability to perform certain movements in order to protect us from injury.
The video shows a few options for teaching your core to fire before performing the movement.