So, what is the reason?
The reason has to do with the placement of the Earth and the Sun. The Earth circles around the Sun and it takes 12 month (and 12 signs) to go full circle. While the Sun spends time in a certain sign, the earth is just in the opposite side of the sky.
Therefore: You can see the constellation of Sagittarius when the Sun is in Gemini and you can see the constellation of Gemini while the Sun is in Capricorn.
Read more about it here: http://astronomicaluplands.blogspot.com/2011/04/constellation-of-month-gemini.html