What is actually so bad about classical shoes?

• Wrong shape: today, almost all shoes are designed and produced much too narrow because narrow shoes are commonly thought of as sleek and elegant. The disadvantage is that your foot and toes cannot spread when touching the ground as they should. Most shoes are even so narrow that the pinky toe is forced to bend inwards instead of being allowed to grow straight. 
• High heels: This is also true for most men's shoes by now: the heels are 2-3cm high, and this has been commonly accepted - and why not, everybody likes feeling taller. And for women, high heels are commonly thought to make them appear more attractive. But high heels are horrible for your feet, and even your whole posture. They lead to shortened Achilles tendons and calf musculature, and at the same time, the back naturally has to move into a much to hollow position to keep your body in balance and prevent you from falling forward.
• Shoes that are bent upwards in the front: With some shoes, especially Running shoes, I have observed recently that their whole shape is bent to a convex shape (allowing it to seesaw/teeter like a cradle). This shape is the exact opposite of what your feet should do to soften the impacts. Your feat naturally want to form an arch, but the stiffness and shape of the shoe sole prevents that completely.
• The insole: I am sure that shoe salesman have already advertised to you the fantastic comfortable insoles of their shoes. And admittedly, when you try them on, those insoles usually feel quite comfortable. But it turns out that they are really bad for your feet. In German, the insole is called "Fußbett", which literally means "bed for your feet". Your feet muscles are not needed and can rest, which is nice for a few minutes, but over time, this also means that they will degenerate.
• Lack of flexibility: All who run or even sprint with barefoot shoes know how much flexibility and mobility in your feet is needed for such complex movement patterns. With classical shoes and their thick soles it is really hard to run properly, and sprinting is hardly possible. Your foot is in a "prison" and cannot move as it should. 
• Many running shoes support what is known as supination: supination refers to turning of the sole inwards, shifting weight to the lateral edge (wikipedia). This is something that your feet should do naturally when running. Classical running shoes, however, are built so that your feet stand in there askew - the inside part is higher than the outside. This leads to higher strain and a greater risk of injury. If you are used to barefoot shoes, you will immediately feel pain after running a short distance with classical running shoes. 
• For all hikers: A common saying in Austria is that "hiking shoes are important for a secure foothold so that you do not sprain your ankle". Extreme hiking shoes go up to the middle of your shins. A 2cm-thick sole and a particularly stiff upper material provide the "secure foothold". Lace the shoes really tightly, and the disaster is complete. You packed your foot in something where it cannot move at all any more - and this is supposed to be good?? Personally, I go barefoot onto most mountains and bring a pair of barefoot trail running shoes just in case. And for the higher mountains and snowy parts, there are also barefoot hiking shoes available. Even without shoes, I never sprained my ankle hiking - the only think I have to take care about are thorns or sharp stones. 
• Knee issues: as already mentioned in other posts, your feet should already reduce the impact by more than 50% with the barefoot running technique. This means that your legs, especially the knees and hips, are strained significantly less. I used to have hip pain when running with classical running shoes, but now with barefoot running, it just does not come again.

 Summary: 

We willingly put "prostheses" on our feet which we would not need from the beginning. And at some point, we will depend on them, because our feet musculature is gone, and our feet start to become more or less crippled.
There are several studies that show that the risk of injury is much lower for experienced barefoot runners than it is for runners with classical running shoes. I will summarize those studies in a separate post.