I know that spinlocks work with spining, different kernel paths exist and Kernels are preemptive, so why spinlocks don't work in uniprocessor systems? (for example, in Linux)
If I understand your question, you're asking why spin locks are a bad idea on single core machines.
They should still work, but can be much more expensive than true thread-sleeping concurrency:
When you use a spinlock, you're essentially asserting that you don't think you will have to wait long. You are saying that you think it's better to maintain the processor time slice with a busy loop than the cost of sleeping your thread and context-shifting to another thread or process. If you have to wait a very short amount of time, you can sleep and be reawakened almost immediately, but the cost of going down and up is more expensive than just waiting around.
This is more likely to be OK on multi-core processors, since they have much better concurrency profiles than single core processors. On multi core processors, between loop iterations, some other thread may have taken care of your prerequisite. On single core processors, it's not possible that someone else could have helped you out - you've locked up the one and only core.
The problem here is that if you wait or sleep on a lock, you hint to the system that you don't have everything you need yet, so it should go do some other stuff and come back to you later. With a spin lock, you never tell the system this, so you lock it up waiting for something else to happen - but, meanwhile, you're holding up the whole system, so something else can't happen.