Sorry late to join in on this one….I recently had a similar experience with a pushy parent. Their back ground was teaching in another musical instrument where the belief was that it was all to do with grades. So tricky! I stated what I believed was best and had to really stick to my guns.
I was happy to offer to help the student take their pre grade test in singing (prep test ABRSM) that gives children the opportunity to see how an exam feels without any pressure of pass/fail. This was a good first base, and a few exam boards offer pre grades which are useful. It went well and the experience was enjoyable. The parent wanted me to carry on heading towards grades but with very little lesson time. This just was not feasible or realistic for either myself or the child. As they were unable to meet my terms we had to part ways.
I think if parents cannot see that the teacher is the expert and knows what is best for each individual student then this is a tricky situation to be in and really difficult as you need them to listen to you. At the end of the day the child’s happiness, confidence and development musically is the teacher and parents responsibility. If a parent is not wiling to listen and follow advice then I agree with Eliza, an alternative teacher needs to be sought.