One argument for Cessationism is that if the Holy Spirit continued to inspire words today, those words would have to be taken and added to Scripture. This would be, at best, problematic for us. An excellent counter point to this is that even historically, not every inspired word of God became Scripture.
Of course, we could throw in the obvious point that not even 100% of Jesus' words have been recorded. In my eyes, there is nothing more "inspired" than the words that proceeded from Christ's own mouth. Even if you want to argue that inspiration doesn't cover words that proceed directly from the mouth of God, it can be assumed that someone would reiterate something He said. Maybe Mary even recorded His first words. "Joseph, He said mommy!"
But even before Jesus was born, there were many prophets whose inspired words were not recorded. Case in point, while there are a mere 66 books in Scripture, 1 Kings 18:4 tells us that Obadiah managed to save 100 prophets from the massacre (i.e. more than just one or two dead) lead against them by Jezebel. That's a fair few prophets, and we don't even know their names, much less what God inspired them to teach.
At this point in time, I personally do not know where I stand on Cessationism. Until a few years ago, I would have called myself a Cessationist, but only by inheritance. I was not committed, nor could I defend that position. However, I do recognise poor arguments when I see them, and so if I am to weigh in on the issue at all, this is what I have to say. Examine every issue in depth, and try not to form hard opinions before you have done so. Test everything, and hold on to that which is good, searching the Scriptures daily to find out what is true, for this is what scripture itself commands (Acts 17:11; 1 Thessalonians 5:21).