Parents must be supportive of the coach and the team. But it's a natural thing that parents are most concerned about their own child. Most parents are really good people who are just trying to do what's best for their child... as it should be.
The coach, on the other hand, is first concerned about the team and secondly about individual players. Now a good coach will care and a show real interest in each of his/her players individually, but the team always comes first.
Parents are rarely objective. Most parents honestly believe their own son/daughter is better than he/she really is. They see all those uncontested shots made in the driveway and flashes of game highlights in the past, but they don't know what is happening in practice.
Parents want to see their own child playing a lot of minutes. On the other hand, coaches are trying to win. So a coach is going to play those players that will help his team win, those players that are performing best in practice and have good attitudes and come to practice. This is especially true with high school varsity level teams and "performance" type club (AAU) teams. Youth "participation" type teams will try to allocate playing time more evenly, although the better players will almost always play more.
Parents, don't be a "know-it-all". Criticizing other players in order to make your own child look better is always a bad thing. Undermining the coaches, trying to make yourself look like a basketball authority, will only hurt your child... if it gets back to the coach, your child will probably play less, and if you voice your opinions to your child, he/she will lose respect for the coach and his way of playing the game, and will most likely not play as hard in either practices or games. Remember that there are many ways to play the game, many styles... the one you like is not necessarily any better.
Parents, don't bother or yell at the coach during games. We have a 24-hour rule wherein a parent can have a discussion with the coach, but not right after a game, not until the next day. It is unwise to have a conversation immediately before or after a game in the gym when emotions are running high.
Sleep on it, and then talk the next day... oftentimes things look different, less important, in the morning and by then usually both the parents and the coach are rested, more receptive, rational and respectful.
Parents, don't interfere with practices. Practice is like a class and the gym is the coach's classroom. The coach might allow you to watch, but keep a low profile.
Playing time issues... we will discuss almost anything with parents, but playing time is not open for discussion with parents. We make this policy known at the first parent-player meeting in the pre-season. Parents cannot be objective, and do not know what is happening in practice. A player may discuss playing time with the coach, but not parents... that's our rule (high school level).
On the other hand, coaches must be willing to discuss other problems and issues with parents. Again, most parents are good people who just want what's best for their child, just like we all do. So be willing to meet with parents, be receptive and respectful.
Do not be condescending or arrogant. A parent should be able to talk to a coach much like he/she should able to talk to one of the child's teachers. And remember also that losing the support of parents in general has cost many an otherwise good coach his job. So be open, patient and understanding.
If a parent makes suggestions regarding strategy, plays, offense, defense, etc... let him "play" on and get his 2-cents in and then thank him, even if you don't agree and even if it really gets under your skin. If you want to get into explaining why you do things the way you do, OK... but it's easier just to thank him for his thoughts and leave it at that. Don't get into an argument about it.
When parents and a coach have a private discussion, listen to each other's concerns and be respectful. Don't necessarily try to change each other's opinion, but just explain your thoughts and feelings regarding the issue... why as a coach, you are doing what you are doing. Or why, as a parent, you are concerned.
Coaches, remember that unhappy parents can make you very unhappy.
Also see... Parent - Coach Relationship