The biggest reason you shouldn't watch it backwards is because episode 25 does not follow the reverse chronology time order so it will ruin the rest of the series for you. The later episodes, 19-26, are generally better than the earlier ones so if you watch it backwards, the series loses steam as it goes on.
People are tempted to watch it backwards because the plot is really hard to grasp in the first few episodes. Truth be told, the plot is not the main reason to watch this show. It's a decent plot full of mystery and supernatural suspense, but it has its share of plot holes and slightly jumbled plotlines. Without the unique format of the show, Touka Gettan would just be another mildly entertaining and undistinguished fantasy drama.
Watching Touka Gettan the way it's meant to be watched gives the viewer an appreciation of the way the story has been molded to fit the format. You can easily see where this format succeeds in bringing something unique to the story, and also where it fails. It challenges the viewer to reevaluate his own expectations when watching an anime. When you see a character as they are introduced into the storyline, you realize that that constitutes the end of their role in the story. Most everything they will contribute has already been covered. Instead of waiting for the last episode to see if a certain plotline gets resolved eventually, you're made to be aware of the entire lifecycle of plots being introduced and resolved as the series goes on.
Aside from the format, the anime has several things going for it. The animation is very lush and it sets a great mysterious mood. There are several episodes near the end presented in very different and unexpected ways which just adds to the quirkiness of the series. Some of the issues touched on in the show are surprisingly deep and adds a small level of discomfort which is not a bad thing. Some will be turned off by instances of really risque fanservice, but my own opinion is it just adds to the charming strangeness of it all.
Many anime viewers don't really want a challenge when they watch something. A lot of people will not bother with this show because it takes so much effort and concentration to watch it. I think if you can get over that, it's a really unique anime and a great watch for people who appreciate the more innovative side of anime.
