I can be one of those persons who say, "I can't." But I usually try to catch myself and not say it. The "I can't"s really are a symptom of someone being frustrated with what they are learning -- or that they are not learning it as they would like to. If they are new, they may be expecting too much too soon from themselves. Tell them it is okay to be confused. Aikido is challenging. If they were not confused and frustrated then perhaps they are not doing it right (this is especially the case with newbies or when learning a brand new technique.)
The times I remember the most saying it was when I was just learning my rolls -- and most recently learning koshinage. I had an incredible mental block when trying to roll. My problem is that I just analyzed what I was doing too much. I would have so many things going through my mind that I was not able to register my thoughts. I had to learn to let go of my thoughts and just do the technique. But this took time and a lot of effort on my part.
Of course this was very frustrating for me. And whenever I find frustrating moments in my practice, I say to my self, "I can. This is something that is challenging me. Slow down and do the technique step by step." Sometimes in learning to do a new technique one needs to break it down in linear steps then move into the circular flow of the technique. Doing this usually undoes my, "I can't"s.
I hope this helps.