All start of all century will have date like that, and there are 8 of them ascending :
01:02:03 at 4/5/06
02:03:04 at 5/6/07
03:04:05 at 6/7/08
04:05:06 at 7/8/09
05:06:07 at 8/9/10
etc...
08:09:10 at 11/12/13
And as much descending
06:05:04 at 3/2/01
07:06:05 at 4/3/02
etc...
16:15:14 at 13/12/11 (yeah on a 24 hours clock

).
This happens at every start of century. So within our lifetime, unless you are living longer than 100 years *AND* were born shortly before such date you will see it only once.
But for humanity, it will happens every century. In 1900, 1800, 2000 2100...
There is nothing special for humanity in 02:03:04 5/6/7 *AND* there is nothing special in starting with 2 to 7, as next year we will ahve a 3 starting to 8.
Number are funny, you can associate all sort of meaningless stuff to them.
PS: about living a century I hope very soon to wish good birthday to my Grand Mother. Which is 98 years old. I wish I could live as old as her with as much brain as she still have...