Do you consume much media? I ask because I used to be similar to you; I never used to be able to distinguish between 30fps vs 60fps but I find that the more media I consume, the more the difference becomes apparent to me.
Aside from that, one of the clearest videos I've seen the difference in is: https://www.youtube.com/watch?v=C-dOuBcxMlk - the commentary isn't very constructive in that video but I see a rather large difference between gameplay clips.
Aside from that, one of the clearest videos I've seen the difference in is: https://www.youtube.com/watch?v=C-dOuBcxMlk - the commentary isn't very constructive in that video but I see a rather large difference between gameplay clips.