Your question came up in a discussion at the New Scientist office today!  I must admit, my dog has a penchant for my socks - he takes them to make me chase them and play with him. 

However, I'm slightly embarrassed to be answering a question about YOUR panties, but here's my stab at a simple explanation:

Your panties smell like you. Your dog likes to chew things that smell like you - particularly stinkier things - likes shoes, socks, underwear, etc.  Your dog might be bored and want attention by chewing your stuff, or it may miss you and chew your things to feel closer to you. Check out this explanation from the Humane Society:  http://www.humanesociety.org/animals/dogs/tips/destructive_chewing.html

For more about the science behind dogs' scent of smell check out this New Scientist article: http://www.newscientist.com/article/mg20026846.100-dogs-amazing-sense-of-smell-down-to-a-wet-nose.html

Although he destroys your stuff, you'll be happy to note that your dog is better than a cat. http://www.newscientist.com/article/mg20427381.200-dogs-vs-cats-the-great-pet-showdown.html?full=true

Thankfully, I have no experience or knowledge of mice chewing my panties. Anybody else care to chime in?

Hi Kim, 

Thanks for your response! I guess that might explain dogs, but what about mice? I am more interested in the chemical components inside the discharge that attracts these animals. (Not just of mine, but also of other women's who have had the same problem.)