This is an interesting question, however very subjective. There are no set 'correct' or 'incorrect' answers, unless this question is linked with a broader concept that you have been learning about? But here would be my answer...
Firstly, I do believe this is impossible. But this is a pretty closed answer, unless I give reasoning. It also depends what you mean by harmony? In this answer I am assuming you mean no conflict- so forgive me if I have totally misunderstood.
1- Oppression
It is inevitable that people will have different agendas, or motives for wanting to do certain things. This causes conflict, obviously including negative conflict. To achieve 'Harmony', some people would have to compromise on their beliefs and actions- and how they live their lives. Who would be the ones compromising? If there was complete harmony, these people would be unable to question this, or even unwilling. People would most probably become 'brainwashed', unaware of the compromises they are making in their lives. This brings up another very interesting question- Is peace and harmony more important than free will?
2- Extreme boredom/ lack of meaning to anything
Would harmony even exist if there was no conflict? To put it in other words, how would you explain harmony without referring either directly or indirectly to conflict?
What gives people the drive to fight for what they want? Not all conflict is negative, and one conflict can appear positive to one person, and negative to another.
What would we do all day? Many jobs would simply cease to exist- Lawyer? No. Relies on conflict. Social worker? Same thing. Even less obviously linked jobs such as musicians, teachers, politicians, athletes, would be affected. Ever noticed how on the news, many of the stories are about conflict? That is what interests us. Gives us something to debate about. There would be no diversity in culture, perhaps we would all be vegetarians or vegans (if 'everyone' refers to all living organisms on earth). Upon further reflection, harmony doesn't seem as much of a 'utopia', or perfect world, as perhaps it first seems
