This phobia is an extension of Triskaidekaphobia which is the fear of the number 13.
It is derived from the Greek word for Friday - paraskevi.
Relevant on the day to raise the matter then. Semantically the extension of the name for one phobia into a connected phobia is interesting in itself. Of course, as in the case of most phobias, there is little basis in logic for this phobia but there could be theories that give reason.
The Last Supper
From the 1890s, a number of English language sources relate the "unlucky" thirteen to an idea that at the Last Supper, Judas, the disciple who betrayed Jesus, was the 13th to sit at the table. The Bible says nothing about the order in which the Apostles sat, but there were thirteen people at the table.
The historical reason is actually not that logical anyway as the attributes of God were the Thirteen Attributes of Mercy. In fact there are older theories for the fear of 13 going back to the Vikings and Babylonians. They are just theories.
There have been some noteworthy events that have occurred on the date;
Apollo 13 suffered an oxygen tank explosion while in space on April 13th 1970
On Friday October 13th 1307, the arrest of the Knights Templar was ordered by Philip IV of France.
In 1881 an influential group of New Yorkers led by US Civil War veteran Captain William Fowler came together to put an end to this and other superstitions. They formed a dinner cabaret club, which they called the Thirteen Club. At the first meeting, on Friday, January 13, 1881, at 8:13 p.m., thirteen people sat down to dine in Room 13 of the venue. The guests walked under a ladder to enter the room and were seated among piles of spilled salt. Many Thirteen Clubs sprang up all over North America over the next 40 years.
To assuage the worries of people who may think there is something in the fear there are other numerically focused phobias.
The number of the beast.
17 is an unlucky number in Italy because in Roman numerals it is represented by XVII which can be rearranged to VIXI meaning 'I have lived' a euphemism for 'I am dead'.
Tetraphobia is a fear of the number four and seems to be common in Asia and south-east Asia.
39 is a number of shame in Afghanistan.
So there are lots of examples and the converse is true. In Japan 8 is a lucky number and in some regions, eg Italy, 13 is a lucky number.
Colgate University in New York State was set up by 13 men each with $13 and 13 prayers. Their luckiest day of the year is Friday 13th.
Lots of opportunities to allow inspiration to blossom!