It’s because of the material of the arrow vs a bullet. A bullet have more energy than an arrow, but the tip of the arrow is usually made a steel, while a bullet is made of lead with a copper layer on the outside. At lead the usually bullet that people shoot. The bullet proof vest is designed to deform the bullet and redistribue the force over a large area. But an arrow is made of a stronger metal that won’t deform, but instead will pierce the boby armour.
At least that’s what you get if you look at a body armour designed to stop a large pistol caliber. Here a video of a level IIIa body armour.
[https://www.youtube.com/watch?v=sFUWkNOnxqU](https://www.youtube.com/watch?v=sFUWkNOnxqU)
That said, there is stronger body armour able to stop a rifle round or even an armor piercing round. I doubt that a crossbow would be able to stop those, but I would depend on the strenght of the crossbow and the distance of the shoot.
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