I agree that you should stick to the simplest reasons – scheduling conflicts and not having enough time. I have had to do this same thing a few times for various reasons. Each time it’s good to give them other teacher names and numbers. I usually give each student a little parting gift and make sure they don’t feel rejected in any way. Putting everything in writing with a specific date when the lessons will cease is helpful. Overbearing parents may keep pressuring for one more lesson. I have found that it’s important to never allow parents to stay for lessons. This almost always results in trouble. I don’t know if that has ever been an issue for you. Teaching in the home instead of a school environment can sometimes result in a more relaxed, less structured environment which can bring out more discipline problems in students and more intrusiveness from parents. I had one student who used to chase my cats around the house. I do think that teaching can be some of the most rewarding work, but I don’t tolerate disrespectful behaviour. No one should. It’s better to save your energy for people who appreciate what you have to offer.
This is the type of thing I have told parents whose students I can no longer teach:
“Recently there have been additional responsibilities placed on me that will make it impossible for me to continue teaching the large number of students in my studio. I have appreciated the opportunity to work with your child, but it is now necessary to transfer your child to another teacher. Enclosed is a list of names of teachers who I respect and admire. You child will be in excellent hands. I am disapointed that circumstances have made this necessary. The last lesson will be on ___________ . Please let me know if I can be of any further assistance in the transfer process. “
Fortunantely no one has ever tried arguing with me when I present it in a simple and final way. Good luck.