The order of succession was established by the Constitution, and it probably seemed a good idea at the time. The House is ostensibly closer to doing the will of the people, so I suspect the framers reasoned that the Speaker would be the better choice, as maggiesmom1 suggests.
Incidentally, the third in line for succession is the President Pro Tempore of the Senate, not the Majority Leader. The President Pro Tempore is a position established by the Constitution. Whoever holds that position presides over the Senate when the Vice President is not present. The Majority Leader has no constitutional powers that I’m aware of.
After the President Pro Tempore, the order of succession goes to the cabinet; I believe beginning with the Secretary of State. Alexander Haig once quipped that he was “in charge” after Reagan was shot and Quayle was not available. He was chided in the press for not being aware of the order of succession.