When you think of all the people who have lived on our planet, or even the ones who have achieved some modicum of fame, it may seem that a biographer has a dazzling array of choices. In fact our choices are restricted in a number of ways.
Most obviously, there is little point in embarking on a biography of someone who has left few traces. Without a sizable number of surviving documents and news reports it's hard to see how a life can be reconstituted on paper.
Then there are problems of access: the widow won't allow you to read the journals; the bulk of the correspondence is in the attic of someone who can't be bothered to unearth it; the subject's archive has embargoed the papers until 2060; none of the colleagues or relatives are willing to be interviewed.
A biographer also needs to consider whether the life is sufficiently eventful, at least during the period of the subject's major achivements. While a great writer can make sitting in a room and thinking sound fascinating, most of us depend on the ebb and flow of life events—including shifting relationships with lovers, children, friends, and people in power—to make our narratives come alive.
Another roadblock is the tyranny of trends in publishing. If you are writing about an obscure author whose books are out of print, it's highly unlikely that a trade publisher will accept your proposal, though you might have better luck with a university press. But if your forgotten author wrote about women or people of color in ways that are now considered offensive, you will have a hard time convincing an editor that the world needs to read about him—no matter how otherwise significant his books are, or how seriously you intend to discuss his failings.
If you choose to write about someone famous, the burden is on you to prove that you have a fresh angle, usually the result of a newly discovered trove of papers. Historical subjects require familiarity with current scholarship; specialized fields such as art demand a working knowledge of the language used by practitioners.
Most discouraging is the roadblock that appears after you already have done a great deal of research but before you have secured a publishing contract: the publication of another book on your subject. Unless you can figure out a way to enlarge your topic or otherwise drastically alter your approach, the only thing you can do is move on.