I have had this told to me since I can remember - that shaving your hair makes it grow back thicker. It's a myth that has caused many women to turn to alternative hair removal methods for fear of growing thicker hair. I have also found it on Snopes. After doing some research, I have found that this is,indeed, a myth. However, the hairs do grow back more noticeable than before. It is true that after shaving your body hair, it may feel slightly rougher or coarser than you remember. This is due to the fact that hair that grows naturally have a wispy, tapered tip whereas hair that grows after being shaved have a rectangular, blunt tip. This makes the hair seem thicker and darker than before you shaved even though in truth, the width of the hair is the same. According to scientific thinking principle 3, a claim is only meaningful if it is falsifiable. In this case, the claim is falsifiable because it can be tested. In fact, it has been tested and proven otherwise. Apart from that, the study is replicable as all findings based on the matter have been the same.
Other than that, in my opinion, having hair grow after a few days of not having hair at all will definitely make the hair seem more noticeable. An analogy for that is coming out into a bright area from a dark room. Everything will seem extremely bright because your eyes aren't accustomed to the light yet. In the same way, you are used to having no hair so that when hair grows, it seems extremely coarse and dark relative to what it was before. This could be another explanation as to why hair SEEMS to grow back thicker after it's shaved.