Supreme court judges should go through the same election process as Presidents, Senators, and Representatives. Why should they be picked by the president and skip an entire election process. The people should have a say in whether or not a judge will be voted in, especially since they have a life term.
Elected judges must adjudicate in ways that will please their constituents, and may not always try to purely apply the law. The party in power can try to stock the court with judges of a specific type - conservative, liberal etc, which is not always a positive thing. However, while Supreme Court judges are political appointees, there are a number of built in balances in the process - party changes and party resistance on the confirmation hearings. Appointed judges do not have to issue opinions based on a need to be re-elected.