Druid type of armors.
One looks to be a picture of bug parts.
One is made from wood.
Other from crocodile hide.
Last picture is one of an imagine of a Celtic druid in which the druid class was modeled off.
Metal Armor.
One is of platemail
Other is of chainmail.
Last is of scale mail.
All the material has been altered but in different ways. Bug armor, wood, and hide there is no real changing of natural properties. Just some re-working. Like I skin a bear and make a coat. I don't change the properties of the bear's fur or alter it drastically. Wood is shaped by wood tools. You get the idea.
Metal on the other hand is changed drastically from its natural state. It is refined. Iron is mixed with carbon to produced steel. Copper is mixed with tin to produce bronze. Same thing can other metal alloys. The forging process is quite in intensive and changes the metal atomic structure. So a finish product is much different that its natural state. Metal is manufactured.
A druid was a spiritual leader for his/her people. The Celtics had their warrior that used metal armor and such. Not everyone was a druid. A druid chose his/her path to follow and be one closer to the earth. So, in the arguments of a druid would say something along this.
"I wear the protection that nature provides me, not man."
This idea of being close to nature is what makes a druid a druid. Not a fighter or a cleric. That is why they have an oath. An oath to be close to nature or one with nature as it would be.
A knight, fighter, or paladin would probably choose the best protection he/she would get. Hence the metal plate mail. Its because they are trained and they face many opponents with sharp things that are trying to kill them. I don't see them going after bug parts.
The shields don't bother me because there is no real metal shield unless you consider the Mirror Shield. And some metal has to be used in making a shield. Rivets and stuff to hold it together.
But for a druid to willing put on a manufactured steel so that he/she can charge into battle is crazy. Druids don't have to be in thick of battle. That's why they have animals and their followers to help support them and they wield the power of nature. That's right all you druids, get yourselves a few followers to help you. Excellent RP and you don't have to violate your code.
Enough said
I hope this explains why the PHB says the druids can't wear metal armor. And if you play a druid think of what it means. Same with paladins and clerics.