I am told to avoid writing one-sentence paragraphs. What are some good reasons for following this rule?
There is nothing wrong with writing a single sentence paragraph, so long as that sentence communicates the desired message.
The UNC Writing Center says:
Paragraphs are the building blocks of papers. Many students define paragraphs in terms of length: a paragraph is a group of at least five sentences, a paragraph is half a page long, etc. In reality, though, the unity and coherence of ideas among sentences is what constitutes a paragraph. A paragraph is defined as “a group of sentences or a single sentence that forms a unit” (Lunsford and Connors 116). Length and appearance do not determine whether a section in a paper is a paragraph. For instance, in some styles of writing, particularly journalistic styles, a paragraph can be just one sentence long. Ultimately, a paragraph is a sentence or group of sentences that support one main idea.
Since each paragraph supposedly has a purpose for being, at least one sentence would be needed to state that point. Additional statements would usually be required to elucidate, expand upon, or support that idea. A one sentence paragraph would probably either be excessive in length or insufficiently expressive of the idea.