My puppy loves to chase her tail and bite it. I've been reading training books and they all seem to say to distract her from that. Why is it bad for a dog to chase it's tail? I thought that is a natural thing dogs love to do.

There is an incredible amount nonsense around on the care and training of dogs. Many very good people see nothing wrong with it as long as the dog isn't excessive about it. Many of my puppies have done it and gone on to successful careers as dog guides.

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My dog loves chasing tail and I don't think there is anything wrong with it, when he's bored and waiting for me, he'll chase his tail, it's like having an attached toy for him.
I think it only becomes a problem when he start chewing on it and you see fur loss, that could be an indication of an allergy to their food.