As written, the income tax is actually an excise tax that is -or should be- avoidable if one doesn't engage in federally excise taxable activities. So in that sense, it is indeed voluntary.
Unfortunately, in practice, the income tax is so widely misunderstood that it has come to be mis-applied and effectively enforced as an unavoidable direct tax.
For those who are interested, there is a great book on the subject entitled: "Cracking the Code- The Fascinating Truth About Taxation In America", available for purchase here
There is also a wealth of free information available at the author's website:
Edit: I was responding to the title and the description of the video, but hadn't watched the video. I decided to watch it and had to go back and change the title of my comment (it originally read "Well, technically, he's right"). Reid is talking non-sense. He probably doesn't even know the true nature of the tax.