Not necessarily. It depends on what you define as cheap. Are you referring to cheap in the sense that it's an inexpensive product or cheap in the sense that the product is of inferior quality? I have purchased many inexpensive products over the years and they have worked perfectly fine for me. Why spend $50 on something when I can get something that does the exact same thing for $5.
If you are referring to a product of inferior quality then there is a chance that it will break, yes. But there is still the chance that a product of more superior quality will break as well. The charging cable that came with my Ipod (official apple cable I suppose) is all sorts of cheap crap. the white protective casing around the wires started coming off not even a month after I got it and the cable is now unusable. I could have purchased a replacement from Best Buy, again an official apple cable, for $30 but I instead chose to order a $2 cable off ebay. the $2 cable works much better than the apple one and it has yet to fray or break after ~2 years of use.
Your argument is flawed. Go back to school.