Can you? Yes. Should you? Probably not -- unless there is a good reason to do so.
Quoted phrases in an essay are primarily used to cite the exact text of an external source. If you are only citing your own opinion, it can be confusing to set the text apart with quotes, because the reader may naturally assume that you are referring to someone else's words, and expect you to give proper credit.
The point is that you always want the reader to think about what you have written, and only about how you have written it if that is your intention. I would keep it simple:
This naturally raises the question: Why set words and phrases apart with quotes when they only represent one's own personal opinion?
That being said, it depends on what formatting options you are allowed to use. Consider this forum, in which you have a number of options other than quotes, including italic, bold, bold italic,
subscript, superscript, and probably many more I don't know about. Because you have options, you don't always have to use quotes to set your text apart. However, in a formal written essay, your options be more restricted. If that is the case, it's fine to use quotes to set apart any text that you want to keep as a cohesive block:
The question you should ask is not, "Why set words and phrases apart with quotes when they only represent one's own personal opinion?" but rather, "Will the use of quotes seem natural, or awkward?"
In the end it does come down to personal choice, but choice based on convention.