Why does the director of graduate studies want me to keep my TAship, even though I obtained a scholarship of my government? I am a first year math phd student. I could get a scholarship from my government and notified the director of graduate studies of my department (which is now my provisional advisor) that I wish to decline my TAship position for the next term. He advised me to think more about it and told me to think about it 2 more weeks. He told me that I should keep being a TA.

Well, my TA duties are a burden and I do not learn nothing of math from it. Besides that, it drives me crazy. I do really detest having to deal with those undergrad students. I prefer to devote myself to learn and then do my research. But my advisor wants me to think more about it, Why? If I am not a TA, I could have more time to work on my advisor's projects. Besides that, I do not think my department would have any trouble to find another TA. My school is not Harvard but it is ranked among the 30 best of USA, so there is a lot of people that want to be a TA there.

Why does my advisor want me to keep being a TA?
You need to ask your advisor, since nobody else can say for sure what his reasoning might be, but here are some possible explanations:


You do a great job as a TA, much better than whoever might replace you, and the department would be unhappy to lose your services.
You do a poor job as a TA and need to take this opportunity to improve your teaching skills before they interfere with your career.
Having more teaching experience on your CV or better teaching evaluations may help when you apply for jobs, even aside from whatever you might learn in the process.
If you "detest having to deal with those undergrad students", you may be miserable working in academia.  It's much better for you to figure out now whether/how you can handle teaching successfully without having it feel like a huge burden.  Delaying confronting this issue isn't necessarily in your best interests.