What is the consequence of “prematurely writing people off as failures”?

The quote referenced in your question comes from chapter 1 of Outliers, which explores the balance of hard work and opportunity that ultimately determines one's level of success. Chapter 1 examines the phenomenon by which people born in the earliest months of the year are more likely to become major league baseball players. It would be easy to write this off as a random occurrence, but Gladwell posits that these athletes get an extra year of training because they are born before the cutoff. Think of someone who is the oldest person in your class because of their birthday, just shy of the cut off for the next grade. This person would graduate high school a little later than others and benefit from an extra year of baseball practice before being up for the pros.
This example is used to highlight the consequence of "prematurely writing someone off as a failure." In so many scenarios a person might be rejected—from sports or any other opportunity—who was simply too young or just needed more time to practice, grow, and develop. Gladwell uses Canadian hockey as a positive example of this. The way youth hockey is structured, Canada allows players to start young and to grow and develop their talent in a confined rank before moving to the next level.
Gladwell terms this theory the Matthew effect after this verse in the bible: "For unto everyone that will be given, and he shall have abundance. But from that hath not shall be taken away even that which he hath" (Matthew 25:29). The Matthew effect is basically defined as the cumulative advantage of capital, whether that capital comes in the form of monetary resources or the luxury of time to use for practice and growth.