One of the most difficult tasks when it comes to background removal is irregular shapes or tiny details, such as hair, fur, wool, or similar, but they are important and should still be there after the image editing. It is possible with the proper tools and a little tedious work, but not a secret, if you want to try you can do it with the refine edge tool in photoshop.
For the image below, I’ve had to use the refine edge tool, but to get a more accurate result I’ve had to use it in combination with other tools such as adjustment level and curves layers to highlight the finest details. Notice the before and after, how the image didn’t loose its even tiniest details on the new background.
If you would like accurate editing for your images, but do not have time enough to go through the tedious process of having to learn and use these tools, then I can help you with a precise editing at a very affordable price.
For more info on my editing services,please have a look at my gigs: https://www.fiverr.com/imagedefine