So you just enrolled at a BJJ gym, perhaps been there for a while but your instructor never rolls with you and he seems to always pick who he rolls with?
There are a couple of legitimate reasons why this can happen.
Spazzers
One reason can be you are still spazzing a lot. Spazzers are generally white belts who have not yet learned that they should not be muscularly contracted all the time and generally try to crank on limbs and necks way harder than they should. This is why it’s widely considered that sparring with white belts is riskier (injury wise) than sparring with more experienced practicants.
Injury history
A black belt on the waist usually means 6-10 years of hard training (sometimes more, sometimes less, depending from person to person). As you will find out eventually or probably already did, grappling takes its toll on the body. Lower back injuries, knee injuries and neck injuries are some of the most common in grappling and unless your instructor is a genetic freak, he can probably attest to having some as well. Depending on the grade of injuries and recovery status, he might not want to roll with people who might further aggravate certain injuries.
Upcoming competitions
Training regimens change with upcoming competitions, especially at black belt level where the standards are very high. If your instructor has an upcoming competition, chances are he will start rolling only with people whom will directly benefit his training in the lead up to the event. Perhaps he is looking only for people with a minimum skill level or even more, perhaps he is only looking for specific skill sets to go against.
Gym population
If your gym is extremely crowded and you are still a beginner, chances are it might take a while until you get to spar with your instructor. At this level, you get the same benefit from sparring anyone who is more senior than you, not only your instructor, so you should look into that too.
Gym etiquette
There are some gyms where students are not allowed to ask their instructor to spar with them. That doesn’t mean your instructor isn’t legit or worth his salt. You will likely see him spar with the senior students and get to check out his skills. While this kind of etiquette is not common in BJJ gyms, there are some that adopt them, some instructors being rooted in more traditional martial arts before discovering BJJ.
The general view of the community regarding this is that an instructor should roll with his students (more often with his experienced ones, less with the inexperienced ones) and should be open to being approached for sparring.
So if you approached your instructor for sparring but perhaps he is not available at the time, chances are there’s plenty of senior students around from whom you can learn things. Remember, if you’re a beginner, you’re far from the point of not being able to learn from blue belts, purple belts or brown belts. Take whatever is available and ask for some pointers afterwards, you’ll likely get good details.
If however, your instructor never rolls with his students, regardless of day, health status, etc then you have a serious warning sign you should take into consideration.
At this point, you should start to look for signs of what the community calls “a McDojo”. A McDojo is a school where the teacher doesn’t have any actual skills and only teaches flawed moves that have little to no chance of success against a resisting partner. There are some signs to look for. If he never spars with his students, always shows the moves on a selective one or two loyal students, acts evasive whenever you ask for details, acts evasive when you ask about his belt lineage, etc. Another big sign to look for is if he is completely out of shape. Sparring in BJJ is a strenuous task for the body, one which makes it get fit quite fast. If your instructor looks rather round, no muscle mass, poor posture and you never see him sparring, there are big chances you are in a McDojo.
In this case, the recommended course of action is to look for another gym in your area, one with a real instructor. As a further tip, you should usually check out your instructors online. If your instructor is a competitor, you will likely find videos with him in competition and some, if not all, of his achievements. If your instructor is not a competitor, you can ask him about his lineage and then use that to verify if he is legitimate or not. Most legitimate instructors will not mind you asking about their lineage, in fact they may be even happy to tell you their story on how it all began for them.