I support Israel, but putting that aside I don't get why every president sets out on this futile errand to bring peace to the Israel.
Yeah, it's not actually our job, as a foreign power, to resolve their problems or tell them what to do. If they're going to have peace, they'll have to work it out themselves. This is not to say we can't help, but ultimately it'll have to come from the parties directly involved.
Land for peace doesn't work.
Oh, I don't know about that. Imagine if Canada invaded and took over the state of Michigan. We'd go to war with them to get Michigan back. Michigan would be the issue, and the U.S. probably would not even consider peace until they returned Michigan. Once Michigan was returned, the chance for peace would suddenly improve dramatically. Land may not be the only factor in establishing peace, but it is very important to people.
Why 1967 and not 1000 BC?
Probably because 1967 is within living memory. The Israel-Palestine issue is complex, and I can understand Israel's concerns about security, but I can also see why the Palestinians are upset that Israel would take over those territories (Gaza Strip, West Bank, etc.) and never return them.