The problem is that you have nothing to vote for. In order to vote, there has to be someone to vote for. The problem is that real, sensible candidates are often not even allowed to be voted for. So the question is how to vote for someone you know is a bad choice and at the same time you know that there are no good choices? In order to have a clear conscience, some people refuse to vote in the hope that the low turnout will generate some real resistance and make the situation urgent.
For example, if only 10% of the population votes in the election, the results will only represent this small part of the population, which can lead to questions about the legitimacy of the elected representatives and their mandate to govern.
This is a basis for invalidating the election, and in such a situation, society can feel how many people disagree with the current policy and this can encourage people to greater opposition and rebellion against the current puppets in power.
no matter how many people take part in the elections, they will always say that they have the legitimacy to rule the rest of us
They do, but we don't necessarily :). It's a bit like with covid. In Poland, for example, there was quite a large percentage of people who said it was a hoax and that translated into others also feeling emboldened to counteract.
Simply put, 90% of people are afraid to stick their noses out until they see that they are the majority. If it came to a situation where only 20% of people voted for the government in the elections, there could be a coup, and the currently elected government would certainly be walking on thin ice because people would be aware that no one voted for this government and that practically everyone around them agrees with them. So they would look the government in the eye and chant for its overthrow. On the other hand, if you have a turnout like the one in Poland recently, 74%, people say:
The people have chosen, what can I do? Besides, since you are aware that 74% of people voted and from this you know that 60% voted for POPIS, then you can be sure that every second of your neighbors not only will not support your activities against the current government but can also kick your ass.