Some astronomers announced that they calculated when Christ was born: June, 2 BC. This is based on a conjunction that would have produced a bright star in the sky. There are a lot of problems with this.
First, our image of the nativity comes from a combination of nativity scenes, songs, and centuries-old tradition. We imagine the three wise men arriving at the same time as the shepherds. After all, the nativity scenes show all of them together. At most, they arrived twelve nights after the birth (hence the Twelve Days of Christmas). Outside a star has lit the night as bright as daylight.
Here are some of the problems:
The bible doesn't say how old Jesus was when the wise men found him. Since Herod ordered all boys under two to be killed, it may have been months.
The bible doesn't say how many wise men there were, either. It lists three gifts relating to air (frankincense), water (myrrh), and earth (gold). Since there were three gifts and the ancient world was divided into three continents, that there were wise men from each continent, each one carrying a distinct gift and representing a different age. From that assumption, names and histories were added to the wise men but none of that is in the bible.
We think of the star as being bright but the wise men seemed to be the only ones who noticed it. In an age when everyone was familiar with the stars, it must have been pretty dim to have escaped notice. It is also unclear how the star could have been in the east. Except for polar stars (in the north and south), all stars rise in the east and set in the west. Or, more accurately, the earth's rotation makes them pass by a spot from the east to the west.
The twelve days come from the Roman calendar. They set aside a twelve day celebration called Saturnalia at the end of their year. Christmas replaced Saturnalia but kept some of the older secular traditions. Since this date had nothing to do with the actual birth of Christ, people have been speculating about the real date ever since. Which brings us in a circle.
One thing that we do know, Christ was born. The actual date was not considered important at the time so Christmas is as good a time as any to celebrate it.