The instructions on my guillotine clippers say the same thing - ie that the longer the nail, the longer the quick so you can only ever cut a tiny bit off, and 2mm is quite a lot. Aim for a "slither" or maybe half a mm.
And we should be practicing getting the dog used to being around the clippers, especially if you hurt the dog last time.
As per this video - notice how she trains the dog to sit upside down against her chest so she can easily steady the paw and clip accurately.
YouTube - How to train your dog to relax for nail clipping