You right this is a superstition per your tag. The number 13 itself has a longer history of being unlucky than just the random alignment of Friday with the 13th day of a month. But that is all it really is, a superstition. Dr. Simo Nayha at the University of Oulu did a study on traffic deaths on Firday the 13th as opposed to any other Friday. A telling quote form his study is:
“If Friday the 13th were a bad day, it’d be a bad day for everyone,” he said.
That's because women seemed to have a higher incidence than men of fatal accidents. However, these type of studies are much the same as all the full moon nonsense, and are much more a victim of confirmation bias than anything else.
DePaul University has a whole page on the history:
Now, on to your question, "Why is Friday the 13th so unlucky?" The belief that Friday the 13th is an unlucky day is derived from two long-standing superstitions, the fear of the number 13 and a negative association with Friday itself. The two superstitions are part of a long and fragmented history making it difficult to pinpoint their origin.
The unlucky 13 seems to have ancient origins giving room for plenty of speculation as to why the number came to be considered unlucky. Some theories argue that there are mathematical reasons for the fear of 13, others believe that 13 came to be associated with unlucky events. Whatever the reasons, it is clear that 13 shows up time and time again as the object upon which people have historically projected fear and uncertainty. One of the first texts to reflect this view is Work and Days written by in 700 B.C.E. in which the Greek poet Hesiod mentions the 13th day of the month as an unlucky day for sewing seeds. Unlucky 13 is incorporated in the story of the Last Supper at which Judas was the 13th guest.1
Negativity towards Fridays can be traced as far back as the 16th century in western literature. The term "friday-faced," meaning sad-looking, and "friday-look," meaning a solemn look, surfaced as early as the the late 1500s. In 1592, Greene wrote, "The Foxe made a Fridayface, counterfeiting sorrow." The expression was used again in 1681 by Robertson who wrote, "What makes you look so sad, and moodily? with such a Friday face." Early in the next century Rowley spoke of a "plague of Friday mornings!" in Match of Midnight.2 Why there's a negative association with Friday is subject to speculation.
1) Lachenmeyer, Nathaniel. "The Origins of Unlucky 13." 13: the Story of the World's Most Popular Superstition. Thunder Mouth's Press: New York, 2004.
2) "Friday." Oxford English Dictionary. Oxford University Press, 2008.
Now, there is also an association with 13 being a LUCKY number by some cultures, although the University of Arkansas also acknowledge the unlucky aspect as well. And they repeat many of the same theories as to why it is considered unlucky.
In numerology, the number twelve is considered the number of completeness, as reflected in the twelve months of the year, twelve signs of the zodiac, twelve hours of the clock, twelve tribes of Israel, twelve Apostles of Jesus, twelve gods of Olympus, etc., whereas the number thirteen was considered irregular, transgressing this completeness. There is also a superstition, thought by some to derive from the Last Supper or a Norse myth, that having thirteen people seated at a table will result in the death of one of the diners.
Friday has been considered an unlucky day at least since the 14th century's The Canterbury Tales, and many other professions have regarded Friday as an unlucky day to undertake journeys or begin new projects. Black Friday has been associated with stock market crashes and other disasters since the 1800s. It has also been suggested that Friday has been considered an unlucky day because, according to Christian scripture and tradition, Jesus was crucified on a Friday.
Some may think this is a harmless superstition. Sadly it has real costs:
"It’s been estimated that [U.S] $800 or $900 million is lost in business on this day because people will not fly or do business they would normally do," said Donald Dossey, founder of the Stress Management Center and Phobia Institute in Asheville, North Carolina.
There are other interesting impacts from people's irrational fear of 13. In this question, the answer points out how it impacts economic returns on skyscraper condos in NYC.