In Scrum you never extend a sprint. Read that again. Never. So why do some teams extend their sprint a few days sometimes?
I think the most common reason is there is some functionality that is almost done and it feels better delivering “in a few days” rather than “at end of next sprint”. Might even be so that there is a dependency or hard date deadline that needs to be met. I think this usually is an invalid argument. I don’t think Scrum says you’re forbidden to deliver things to the customer in the middle of sprints. If you really need/want to deliver before the end of the next sprint, do the planning so that you deliver something after a few days in the new sprint instead of extending the sprint.
Another reason I’ve seen is that the team have miscalculated the number of working days they could have anticipated (holidays, team events) and some they couldn’t anticipate (power outages). The reasoning here is that “planning was for X days and since we missed Y we should extend Y working days”. At first glance I think this looks OK. The team is just trying to keep the sprint length consistent. But if you look deeper I think this is also wrong. The team is not looking at the root cause and learning from the failure (i.e. make sure to take holidays and team events into account). Also this is no different than if there is a flu going so that most of the team is sick a few days during a sprint.
Changing the end date for a sprint also introduces another problem. What the team has planned outside work. Personally I tend to plan things like dentist appointments and other meetings during the sprints since I’m more flexible during the sprint. It is my choice if I have to go out for a few hours during the day and I can decide myself to make up for that time in the morning or evening. But between sprints my working day is not that flexible since it typically involves a number of planning and retrospective meetings. Even when I have several days between sprints they tend to fill up quickly with all sorts of meetings. So when the end date changes it is a high probability that some plans I’ve made for the beginning of the next sprint need to be changed too since it is now in a day between sprints.
So what if there is nothing outside work that needs to be rescheduled and adding another day to the sprint means the ability to deliver something much wanted to the customer. Isn’t it worth it? Once? I think you should be pragmatic but in this case I think there are more pedagogic ways to handle this. Handle it as the failure it is, analyzing what went wrong and come up with a plan on how to avoid it next time. Then then take one or two days just focusing on the thing that is so much wanted. This way you are less likely to just accept and forget the failure just because everyone agreed it was a good idea to extend the sprint. And if you find yourself often in this situation, sprints may not be suitable for you. Something like Kanban might be more appropriate for you.