AMM, you hit the nail on the head.
He may be insecure, but he may also be avoiding work. If he has figured out that he only needs to stand close to his trainer to be allowed to just hang out, then he's got her number, and she needs to be forceful in driving him away--not cruel or abusive, just firm.
But I'd like to add two points for consideration.
I suggest starting without a longe line simply because, as a novice, if he does come in or do something like suddenly reverse direction to avoid moving out, you're likely to get tangled in the line, which will cause you to stop for a minute to regroup. That pause could be enough to confuse the horse and give him permission to quit and stand on you again.
Remember to keep your body behind the horse's midline with your visual focus on his hindquarters and the longe whip pointed just behind his hip. You're body language should suggest that you're "chasing" the horse, not just standing there with him. If you're a novice at this, you might be getting in front of the horse just enough to put pressure on him in the wrong direction. Stepping toward his head will stop him, make him come toward you, or cause him to reverse direction, none of which is what you're looking for.
This is a team learning situation where you and the horse are both in training together, so be patient, and reward both him and yourself for any improvement.