Armor take damage when we break blocks with them

Armor or tools? Armor should only take damage in combat for example creeper explosion, being shoot by an skeleton or hit by a zombie. That's also why enchantments are exclusive to certain items.

When I break a block with an armor in my hand, he take damage.

This sounds like normal/expected behavior; when you use a tool that has a finite durability, it wears. If you're using armor as a mining tool, you should expect it to wear.

At least the doors one is a bug and by association I think this is a bug too. If you mine with a stack of doors, the durability of all the doors in the stack goes down. You can tell by splitting a partially worn stack of doors. You get two partially worn stacks of doors. If you mine until the durability of one of the stacks goes to zero, the other split stack will disappear and each subsequent block you break destroys one of the units in the stack you are mining with.