All asteroids should have already been destroyed if the universe was billions of years old ( I don't know if this is some creationist invention though )
I'm going to say probably "creationist invention." It might be an argument based on the Poynting-Robertson Effect, a real phenomenon that really does cause tiny dust particles to slowly spiral into the Sun. But that effect doesn't do much to sand-grain-or-bigger particles.
The other creationist claim I can readily imagine is that all those zillions of asteroids out there should have all collided and pulverized each other "if the Solar System was really old." It's known, in fact, that asteroids do occasionally collide - these collisions lead to "asteroid families" as well as to dust for the P-R Effect to scoop up. I've seen the results of simulations on these collisions in
Science - and the simulations
depend on there being billions of years to give
enough time to give the results, in terms of "families," we see today.
I got intrigued enough by this to come up with a scale model of the asteroid belt at a scale of 1:10,000,000. That makes Ceres, the largest asteroid, a small sand grain about 0.1 millimeter in diameter orbiting 41 kilometers (25 miles) away from a 139-meter (450-foot) diameter Sun. The other 200,000 or so known main-belt asteroids are mostly scattered around in a doughnut-shaped area 20 kilometers thick, 100 km across, and with a doughnut hole 60 km across. A
big doughnut, in other words. And the asteroids are nearly all more the size of bacteria than monsters like Ceres.
The doughnut is big enough, in fact, that those 200,000 asteroids (assuming random distribution, which really isn't so) fill it up to nearly two bacterium-sized grains per cubic kilometer. That's eight per cubic mile. So the chances of collisions aren't as large as antique video games would have you believe.