Declining your manager’s meeting is a different act from declining anyone else’s, and the difference is not politeness. It is that your manager is the person who decides what you work on. A decline is a statement that you have re-decided it, and depending on the manager, that is either welcome, unremarkable, or a problem. ...
Most advice about declining meetings is written as though the only obstacle were finding the right words. Find the polite phrasing, send it, and the meeting goes away. The words are the easy part. The hard part is that a decline is a small political act — you are telling someone their claim on you is worth less than something else — and it has a price. Usually a small one. Occasionally not. The advice that pretends otherwise is written by people who either have no manager or have not had one recently. ...