How should a student defend his 1st authorship in front of his advisor politely and effectively? Inspired this good question, I think posting this question will surely benefit the next generations of students, albeit this does not happen to myself.

The research students will publish several papers along the research road under someone's supervision. When it comes to the issue of the author order, the student and the advisor may not always reach an agreement. i.e. Sometimes the student thinks he or she deserves the 1st author, but the advisor doesn't.

In such cases, the students are usually very worried and upset. Having been working on that topic for such a long time, the student feels very disappointed to be listed as the non-first author. Being the weak party, the student may not even dare to argue with his advisor. After all, the advisor is kind of "in control of" his remaining PhD life. 

Simply put: 

How should a student defend his or her 1st authorship in front of the advisor politely and effectively?
In addition to Peter's answer, one should also keep in mind the accepted practices in one's field of study. For instance, in some fields, such as economics and parts of mathematics, alphabetical order is the default; in other areas, such as organic chemistry, the principal investigator of the lab—not the primary author of the paper—has traditionally been given the first spot in the list.

If you are in a field where the order is somewhat preordained, it's going to be very difficult to change that tradition, for many reasons. In such cases, you should optimize your placement within the "available" options.