Wrong Names of Months

It was in Vienna that I met Prof. Jack. He was a linguist. We were discussing calendars for some time Gregorian calendar, Julian calendar, Hindu calendar, Chinese calendar etc. Then suddenly he popped this question at me. 'Don't you think it is strange. December is the twelfth month of the year. And do you know what actually December means - ten! 'Daka' is a Greek word meaning ten. Therefore, deca litre would mean ten litres and decade means ten years. December then should be the tenth month. But it isn't. How do you explain it? What do you think my answer was?

The early Romans before Julius Caesar from whom our calendar comes from began the year in March. Therefore December was the tenth month. However, when New Year was moved to January 1, the names of the months were not shifted, which caused the disparity between the meaning of the names of certain months and their sequence: 

Here is an example: