There are more days in July to December, than in January to June. So it is a little more likely for a random observer to find himself in the later 6 months.
But if he finds himself before the July, it is more likely that it is a leap year, with an additional day, than otherwise would be.
This increased probability for a leap year skews the probability distribution for the first day of the year also.
This is how it comes.
Correct me if I'm wrong, but isn't the probability of a year being a leap year approximately 25%, completely independent of what month it is? (This seems like one of those unintuitive-but-correct probability puzzles...)
If it's worth saying, but not worth its own post, even in Discussion, it goes here.