Every job will have a certain number of tasks that someone will regard as silly. Sometimes they even are silly. Often they are just things that are necessary for one reason or another but the person being asked to do the task is not necessarily aware of the reason why they must be done or just doesn't want to be the person who does them.
I have seen people regard timesheets as silly, but the corporation needs them filled out to be able to bill the clients. No billing, no one can get paid, not so silly really.
I remember one time when a very junior auditor just out of school thought it was silly for him to make copies of something on the copy machine. He wanted the clerks to do it and the director of the whole organization had to point out to him that junior auditors were the people with the most available time to perform the task and that the clerk he wanted to do it was already over-scheduled. Yes it seemed like a silly task for someone of that profession but, in fact, it was the best use of the resources available. When the way you come to the notice of senior management is through complaining about a "Silly" task you don't want to do, that is not a good thing.
In the case above, it was the guy's speech to give, he is entitled to decide how he wants to present it even if you think it is silly.
Never get into an argument over a silly task. That is counterproductive. You can state your reasons why something else would be a better use of your time or why another technique might be better. But do so calmly and without making a jerk of yourself. You also need to save your credit with your boss for truly important stuff. Arguing for an hour about a silly task that would take ten minutes is "silly". Never strongly argue anything that is not critically important. You want people to pay attention when you object, not roll their eyes because you are at it again.
However, in the long run, someone higher up in the organization is paying your salary and doing these sorts of things tends to help make them into allies not opponents and that is good for your career. Luckily for most of us, this sort of silly stuff gets drastically reduced as you gain seniority in an organization.
So really the best way to handle the infrequent silly stuff is to just do it if they aren't convinced by your initial discussion. It wastes the least amount of time, it creates the least amount of political problems for the future, and generally creates good will and a reputation as a team player. The more junior you are the more important it is to not get a reputation as someone who is going to argue everything.
However, if the silly stuff becomes too frequent (more than 1-2 hours in a week every week as a rule of thumb) or is overcoming your ability to do the job you were hired for, that is a different case. Then you need to have a heart to heart with your manager about what is going to be affected by these duties and if he or she is still convinced the silly stuff is more important, then find out why. If you don't like the answer, then it may be time to move on.