I had a very similar experience, Truth101. I grew up in a Christian school, and it wasn't until High School (when I entered Public School) that I began to be attacked/questioned/disputed. It was that experience that caused me to learn as much as I could about Scripture and Apologetics. I took to debating and discussing things online, and I freely admit a lot of my debates early on were fueled with less than Godly intentions. But the Lord did use them to teach me a lot of things, to come to much understanding, and to make a big difference. Since then, my outlook and methodology and even the intent of my heart has changed drastically.
However I must digress in that in my experience, as long as one maintains their composure (even if the opposition becomes venomous), much good can come out of these debates. It's certainly true that the person you're debating may retreat into themselves and refuse the advice and information you offer, but in most forums, there are a whole lot of people that are reading the topic that aren't posting in it. I've had dozens of people from all over the world contact me outside of the forum to thank me for what I said, that they've decided to start reading Scripture again, that it made them re-think their perceptions of Christianity, etc etc. The Lord can do some amazing things through the internet and debates, I mean, look at Bible Truths.com. The internet is such a wonderful tool. Just think if the internet existed in the time of Apostle Paul or even Christ and what wonders the Lord could have done.
Anyway, there are just so many people out there that haven't taken the time to read Scripture for themselves, and are mislead by clergy, by media, by satire, by detractors. There are so many misconceptions and faulty teachings regarding our Faith. And if you address these misconceptions firmly but with compassion and clear demonstration of the evidence and truth, I've seen even the most staunch, militant atheists go "whoa..you know, there may be something to this Jesus thing after all."
I agree that shouting at each other and quarreling does no one any good, and that it's something a servant of the Lord should avoid. However, if the Lord allows you to maintain your composure and civility and compassion in your heart, there is SO much good that can come of such debates and discussions (as verses 25-26 in the passage Kat quoted say).