You can sacrifice your pet to get pet components at the animal trainer. The higher the pet's level, the more chance you have of getting a part. Some parts are rarer than others. These pet parts are used for making horse armor or a dragon weapon, as well as certain components being used in the Ichi and Scra-Chi pet quests.

You click on the Animal Trainer and this popup window will appear
We want to sacrifice our pet so choose: Harvest Pet Component This popup window should appear.
Again, you want to sacrifice your pet so choose the "Sacrifice Pet" option. This popup should appear. At this point, CHECK if you have equipped the pet you want to sacrifice. BE SURE YOU DONT HAVE YOUR MOUNTED PET EQUIPPED
Push "Confirm" and it will be done. Most of the time you will get the failure message since the chance of successfully sacrificing your pet is very low.
Sometimes you will get lucky and the success message will show.
If you want to know what part you harvest, check your inventory or your system message window. For example, if you got a Dragon Wing then you should see these in the inventory and system message window.

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