A good place to start when trying to come up with essay questions for a text is to think about the themes and the characters in this text and use one of those to base your question on. For this excellent short story, the key theme is that of equality and how human freedom has been curtailed in order to achieve true equality in society. Therefore, if you wanted to focus on this theme, an excellent essay question to select might be:
"Harrison Bergeron" shows the dangers of equality.
This would allow you to discuss how equality is presented in relation to human freedom as it is presented in the text.
If you wanted to focus on a character, the obvious character to examine would be that of Harrison Bergeron himself and how he is so dangerous to society. A good essay question would be:
Why is Harrison Bergeon so dangerous to his own society?
Lastly, if you want a really interesting essay question that will get you thinking, you might like to think about Harrison's protest and how it ended. A good question would be:
Given the ease with which Harrison was executed, what was the value of his protest and why did he behave as he did?
Here are three questions for you to pick from. I hope you find one of these questions useful. I have included some links below to the enotes study section guide on this short story that will help you analyse it further. Good luck!