Comprised of is often called a modern mistake, but it has been in English for centuries. Evidence appears in published writing from the late 1700s, and the phrase has continued to show up ever since.
Why do people object to it? Traditionally, comprise meant include or consist of in a specific pattern: The whole comprises the parts. For example, The committee comprises five members. Because of that older pattern, many editors were taught to prefer composed of when naming the parts: The committee is composed of five members.
In actual usage, though, many careful writers have also used is comprised of, as in The committee is comprised of five members. That use is widespread and well established historically.
- Traditional preference: The book comprises ten chapters.
- Common alternative: The book is composed of ten chapters.
- Also longstanding: The book is comprised of ten chapters.
If you are writing for a strict style guide, composed of may be the safest choice. If not, comprised of is a real part of English usage, not a recent invention.