Sparring is a drill that builds on other skills. If a student doesn't have those skills in place, they aren't ready to spar.
Before a student spars, they need to have a reasonably solid foundation in the tools that they will be allowed to use in sparring. For example, someone who is going to spar Muay Thai needs to know how to punch, kick, knee, elbow (if allowed), and some clinch work. They also need to know how to defend against all of those attacks on at least one level (I like Campbell’s Defensive Hierarchy as a barometer).
What do I mean by a reasonably solid foundation? I mean they should be able to throw any one of those strikes without needing to be cued on what it means (someone who can’t remember if you jab with your lead or rear hand is not ready). Likewise, someone whose response to having a kick thrown at them is to look at the instructor with a puzzled expression isn’t ready either.
How do you build those skills? Shadowboxing, bag work, pad work, and partner drills. Every art has some variation on these things. That’s outside of the scope of this discussion, but those are the things you use to instill the basic tools in your students.
There is a basic level of fitness (in the sense of “being able to do a task”) that is requisite for sparring. Unfortunately, it’s a level of fitness that’s hard to define. I’ve known guys who could run for hours but couldn’t last more than a couple of rounds of sparring. At my heaviest weight of 204 pounds, I could do multiple rounds because I had spent enough time doing sparring that I was still “in shape” for sparring, even if I wasn’t by any other measure.
If someone can’t make it through a few rounds of hard bag work or pad work without getting winded, they might not be ready to spar.
Sparring can be really scary.
A lot of instructors miss this fact, for a variety of reasons. One is that, for the most part, people who think that sparring is scary don’t often become martial arts instructors. The other is that talking about fear or being afraid is frowned on in large portions of the martial arts community. I was very fortunate to discover Tony Blauer and his work, or I might have fallen into the same trap.
There is nothing wrong with students finding sparring scary. That shouldn’t prevent them from sparring at some point, but it may mean they need more time to build up to it.
That's a point worth repeating: IT IS OKAY FOR SOMEONE TO THINK SPARRING IS SCARY. There's a segment of the martial arts community that thinks that any sign of fear is a sign of an incurable weakness, worthy of pity at best, or mockery at worst. Neither is true. Fear is a natural thing. It can be overcome, but you won't learn how to overcome under the tutelage of someone who thinks that it's nothing more than proof that you're a lesser human being. If you are such an instructor, educate yourself. If you're training under such an instructor, leave.
It is up to you as an instructor to judge when a student is or is not psychologically ready for sparring. Some people will be ready the day they walk in the door. Some will not be ready for a year. Both are acceptable options.
If someone is not ready, build them up. If someone is ready, let them work. It's fine to find people's limits, and even push them, but take care that you don't push them so far that you wreck them.