There is nothing wrong with re-inventing wheels. Re-inventing wheels is an excellent educational exercise and a fine way to learn how wheels work. One of the most effective way to learn how some high-level construct works is to have to take care of handling all the low level stuff yourself. It will give you an appreciation for how other wheel implementors did it (or possibly point out some problem in their implementations) and highlight the difficulties of making wheels that work with both racing bicycles and earth-moving equipment. And who knows? you may even invent mag-lev transport.
The problem is with saying "Hmm, I need a new set of wheels for my car. It can't be that hard, I'll whip some up in my basement." and ignoring all the research and testing that has gone into make wheels better over long periods of time, when really, all you want is a new set of wheels. It could work, but you'll probably spend more and take longer than just buying something from your local wheel shop. Most likely, you'll end up with something that doesn't work very well or even ends up hurting you or someone else.
Even more annoying to their fellow mechanics is when someone re-implements a wheel, then loudly proclaims that their wheel is "TEH BEST WHEEL EVAR!!1!11" and everyone else should immediately switch to using their wheel and that anyone who points out that this new wheel has only been tested on a 1957 MG midget, at 25 MPH, falls off randomly and requires buying a whole new set of tools to change the tires is met with "YOU AR TEH SUCK, FIND SOMEONE ELSE TO REPRE#SS, YOU ELETIST SNOB!!!". It may actually even be better, but without compelling evidence, few people are likely to switch.