The video makes a few presumptions that employing common sense must lead to rejecting its premises. The argument that people accept Christianity (or any religion) only because of tradition and upbringing simply dismisses the known fact that people convert from one religion to another. Also it presupposes that every religious person has never really searched out or studied their own religion nor seriously considered the implications if their world view is true. This is also not true. The thought seems to be that if we knew as much as they did we would agree with them. And then the video claims that no one has access to knowledge that others do not. This is definitely not a good argument.
Added to that, I've got to wonder why is the video claims that all religions have equal access to truth and they are fundamentally wrong. It's presented with no evidence that this is the case. This is the point brought up by Mike Gantt in the comments section. He merely points out that the video does not address whether or not Christianity is true or not. If Jesus really is what He says He is then how can that not be reason to be Christian? Many other commenters chastised him for making the comment but his comment points out the only thing that matters. Yes, some people don't examine their lives and worldviews and wonder if they are consistent and true. They should. But that doesn't mean that there are no Christians that have truly searched all over and found no one greater or more worthy of worship than Jesus Christ - Our Lord and Master.
Debunking Christianity: Nine Reasons Why You're a Christian