The first argument that immediately pops into my mind is that teenagers are full of hormones. Often this means lots of physical interaction in their relationships. Teens are already at risk for pregnancy, HIV/AIDS, and STDs. This is because most teens do not have their own doctors they can talk to, do not have appropriate sex-education,etc.. Open relationships just increase the number of partners they are with thus increasing their risk towards all listed above. And you do not have to be having ‘sex’ to get all of what is listed above either (some yes, some no).
A second reason is that teens are so lead by their emotions instead of their reasoning ability (which isn’t actually developed fully until the 20s). They may be making unwise choices purely on what is ‘cool’ or ‘peer pressure’ or other inappropriate reasons.
A third reason is that teens are cruel. There is a lot of jealously, a lot of fighting and name-calling, a lot of a the feeling of invincibility. It is hard for adults to manage the pressure of open relationships. Teens deal with drama every day of their lives and this would seem to create a lot more of that drama. That is more stress and possibly more physical fighting.