Why are some people obsessed with panties?

There are many possibilities here. It could be because they find that panties are awesome. They could have a fetish for panties. Panties might represent something forbidden to them, and we all tend to crave what we can't have or what we think is taboo.

For some, lingerie may represent something in their childhood. Some sexologists believe that there are sensually charged times in early childhood, and if a child, particularly a boy (because of a possibly larger preoptic area in the brain), were to see or experience certain things during those moments, the sights and experiences tend to stick to the child's psyche. Those moments may be forgotten. Then puberty occurs and the increasing hormones and emerging interest in sexuality wakens these moments, even if the person doesn't remember the initial events or makes a connection. Even if they do make a connection, that doesn't give then any more power to resist their impulses.