This is a question that comes up quite frequently. If you do a search function there are lots of helpful threads.
The quick summary:
(A) Traditional teaching is that learning how to operate is actually the easiest part of learning to be a surgeon. Learning the clinical judgment is harder. There is an old saying among programs directors that you can teach a monkey how to operate, but not how to be a surgeon.
(B) On the other hand, technical skill clearly matters, and is going to be a point of increasing emphasis in the future. There was an article last year in the NEJM correlating technical skill with patient outcomes - and more and more research on this subject is coming down the pipeline.
(C) There really are some people who cannot operate. We had someone drop out of our program after essentially realizing this during their residency. This commonly happens after the 2nd or 3rd year as you get more and more experience doing big and challenging operations. These are outliers though. For some it is just poor motor skills, for others it is poor spatial and cognitive processing skills (e.g. cannot picture in their head how a vascular anastomosis should look and where to place the sutures - this resident could place a stitch just fine if you literally pointed where to put it in and where it should come out). There are also practicing surgeons on the very low end of the technical spectrum - the jokes about 007 ("licensed to kill") or HO-DADs ("Hands of doom and destruction") came from somewhere - and residents & OR nurses all know who these people are. In my mind some of them truly should not be allowed to practice, but the system and culture insulate these individuals (at least at the present, though hopefully that changes in a positive way in the future).
So what to do to put this all together? There are truly some people who can't do it - they are in the minority. There are others who can do it, but probably shouldn't. Still the minority but a greater number. There are definitely students who self-select themselves out of surgery when they realize they have low aptitude. But students are becoming so marginalized in the clinical wards and OR that they often don't even get the technical experience they need to figure that out. My advice for you would be to try it out and try to get as much hands-on experience as you can so that you can make an informed choice.