Dance Teacher here - I will try to give you an opinion from 'the other side'.
Without doubt, some teachers are very blatant in their favouritism, however this also happens in other sports and activities and even in schools. This does not mean that all dance teachers favour some students over others. It is true that some 'opportunities' are more suitable for certain students than others, such as auditions, competitions/festivals, JA's etc.
JA's is the Junior Associates of the Royal Ballet School - no teacher is going to send a child to audition who has a 0% chance of getting in to the Associates programme. This would be a waste of the parents' time and money, a waste of the audition panel's time and very misleading and unkind to the child who is being led to believe that they have the necessary requirements to train under the Royal Ballet methods. Teachers screen their dancers carefully and select only those who they believe may stand a reasonable chance, even so out of thousands of applicants only a handful of children are selected each year for the Associates. The same goes for open auditions for musicals, shows and pantomimes - if your child cannot meet the requirements of the audition then it is pointless all round sending them along.
Dance festivals can give the impression of favouritism as some schools select only certain students to take part. As a teacher it can be difficult as you know that the standard is usually reasonably high, even in the novice sections. They are strictly segregated by age, not level, so a 9 year old Grade 1 student who does 45 mins of ballet a week can find herself in the same section as a 9 year old who is in Grade 5/6 level classes and studies for 10+ hours a week. My advice to anyone whose child is being overlooked for festivals - go along and watch your child's age category when your local festival is on. Look at the average ability of the children in the category and ask yourself if your child is of the same overall technical standard as those you have watched, and is capable of remembering a solo of approx 2 - 2 1/2 mins duration and performing it confidently in front of an audience. Confidence plays a large part in festivals I have known some lovely young dancers who would have crumbled on a festival stage due to lack of self-confidence, and others who although capable dancers would not have the self motivation and drive to put in the necessary required hours of home practice.
I do believe that all students in dance should be permitted and encouraged to participate in exams/awards (if not capable of passing a graded exam, a medal test or class award should be offered), and dance shows should be inclusive with every student taking part. I do also feel that no student should be forced into a situation such as an exam / audition / competition where they feel completely out of their depth or placed in a show routine where the choreography is far too complex for their capabilities, but likewise no child should be denied an opportunity or held back from because of unfairness to their peers. Therefore, in some situations it is necessary to be selective.
If you feel that your child is genuinely being excluded because of favouritism, then I would advise speaking to the teacher to find out why, or what areas of their technique your child can work on to improve their chances of being selected in the future. There is also nothing wrong with dancing JUST for fun / enjoyment / a hobby, after all only a few will ever go on to be professional dancers!