when you get a work computer you have to get it set up to do your work immediately. The work you are doing is probably the work you will be interviewing for thus you have everything you need to set up for the coding challenge already set up on your work computer.
When you get a personal computer you do not need to set up all the things you need to do your work immediately, so you will do the setup of things as you need them.
thus if you get a new personal computer it might not be fully setup yet.
If you are of the age that you have kids you may not have time to do any sorts of personal projects, if so and you have an old personal computer it may not be up to date with what is needed for the coding project because you have not been doing a lot of stuff.
If you have kids or other problems your personal computer may end up broken or unusable and you might not have the money at the moment or the reason to buy a new one.
I mean the first one is probably not right either, since often you need to do some particular thing or use some library you are unfamiliar with but it is at least more right than on your personal computer for the other reasons listed.
When you get a personal computer you do not need to set up all the things you need to do your work immediately, so you will do the setup of things as you need them.
thus if you get a new personal computer it might not be fully setup yet.
If you are of the age that you have kids you may not have time to do any sorts of personal projects, if so and you have an old personal computer it may not be up to date with what is needed for the coding project because you have not been doing a lot of stuff.
If you have kids or other problems your personal computer may end up broken or unusable and you might not have the money at the moment or the reason to buy a new one.