A curved Parallel?

My math teacher said that only straight lines can be parallel.
I asked why can't straight lines? She said "because that's how it is."

I dislike this.

Why can't a circle within a circle, where the centres are the same only with a differing radius be parallel? Is a helix parallel?

hlo

http://mathworld.wolfram.com/ParallelCurves.html

Parallel is simply usually defined as a property of straight lines.