Why is the rate at which mutations occur rather slow? I am stuck on this one

Our cells fix them. When they don't we get cancers, not so good. We have loads of checkpoints and DNA repairing molecules and molecular pathways in our cells to make sure mistakes are spotted and corrected.

This is only a taster of the answer, if you look up the cell cycle and DNA repair you will be able to learn further the mechanisms involved.

Hope you find this nudge in th right direction helpful.
:)