Animals, villagers and pets don't avoid block damage.

Examples:

• Horses will roam onto campfires and will stand on them until they die;
• Pet parrots dive into berry bushes and die;
• Wolves will walk through fire to get to you and die;
• Villagers don't avoid fire;
• Rabbits often jump off high ledges and die of fall damage;
• Rabbits will hop face first into cacti.

As personal experience, my best horse was a victim of the first example. It's a dumb way to die.