Do you see yourself in obligation to prove to others why do you choose to be atheist or agnostic.. ?
No obligation. I don't care about converting anyone. I state my stance once in a while, mainly so they'll spare me of their jargon.
Not really. I have tried this before and i have had more success ice skating uphill.
I don't feel I have to justify myself to anyone really but if someone asks.. it's not that I need to prove anything.. other than giving them a rational logical statement on why I feel the way I do. That usually ends the conversation.
I never introduce myself to people and immediately tell them that I am an atheist. Christians will tell you right away and then often will challenge you. If I know something to be harmful to the human condition, then it is my duty as a caring human to say something about it. Religion is one of those harmful things.
Sometimes. I think it's the difference between being an atheist, someone who doesn't believe in a god or gods, and an anti-theist. An anti-theist is an atheist who believes that religions are harmful to individuals and to society at large. See my post a few days ago on this subject. I DO believe that religion is harmful but I also believe in our constitution where everyone is free to believe what they want to. So, while I often don't challenge people's beliefs, I will answer questions when asked and state my case. I will engage in debate conversations as long as the other person is respectful (I ALWAYS endeavor to be respectful) and is willing to listen to my perspective instead of trying to convert me.
Nope. I am secure about my own understanding of things, and don't need anyone else to agree or understand for me to feel good about myself. If I offer explanations it is for fun(seeing other people's reactions or discussing particular ideas intellectually) or because some of what I say might prove useful to someone else.