No, while as a parent myself, I sympathize with your desire to back out, you cannot do so without losing your earnest money/deposit, unless one of the contingencies your refer to specifically allows you to terminate the deal for this reason. Otherwise, the law is very clear that the seller is not liable or responsible for conditions off his property and in the area/neighborhood around the home, or for the identity or actions of other people in the community. A sex offender in the neighborhood is not legal grounds or justification to terminate the contract with this seller.