Some of the rarest kinds of meteorites (achondrites, lunar meteorites, martian meteorites) do not attract magnets because they contain little or no metal. Most terrestrial (Earth) rocks also do not attract magnets for the same reason. Some earth rocks do attract magnets, however, because they contain the mineral magnetite.
A good way to test if a rock is attracted to a magnet is with a circular ceramic magnet like those often used for “refrigerator magnets.” Put it on its edge on a flat, hard surface. If a rock attracts a magnetic, you can cause the magnet to roll by pulling the magnet with the rock.
Don’t use a neodymium (rare earth) magnet. Those things are so strong that they will attract many kinds of terrestrial rocks. An ordinary chondrite will respond to a simple refrigerator magnet.
Throw away your rare earth magnet. Iron meteorites are strongly attracted to even weak magnets.
If you have a rock that does attract a magnet, then it’s probably not a meteorite because magnetite-rich Earth rocks are much more common than meteorites. Cut or break it open. If it has lots of metal flecks or veins like these ordinary chondrites, then it might be a meteorite (but industrial slags sometimes contain metal).
If you have a rock that does not attract a magnetic, it could be a meteorite, but the probability is exceedingly small because nonmagnetic Earth rocks are more common than any kind of achondritic meteorite.