Why did research participants state that they would kill one person to save five when it involved flipping a trolley switch but then refuse to apply the same "kill one to save five: when it involved pushing a person?

Because in the later scenario of pushing a person "the participants used the emotional part of the brain to refuse to push".

The process or act of pushing an individual is far more personal than simply handling a switch, flipping it to do the act. The act of pushing actually activates the emotional parts of the brain which affects our moral decisions.