Currently the "We the People" petition site only allows people to "sign" petitions. If a petition reaches a number of signatures, it is answered by the office of the POTUS.
Adding the ability to sign as "Against" a petition will give the administration a better view of a wider cross section of the population.
Historically, petitions have only had the option to sign in support of a proposal. This caused the people who did not support a proposal to go without a voice while highly vocal groups pushed their agenda.
These "Against" opinions could then be used by the administration to assist it in gaining a better understanding of the opinion of the american citizens in order to accurately follow the will of the people.