We develop a physical model to describe the kinetic behavior in cell-adhesion molecules. Unbinding of noncovalent biological bonds is assumed to occur by both bond dissociation and bond rupture. Such a decomposition of debonding processes is a space decomposition of the debonding events. Dissociation under thermal fluctuation is nondirectional in a three-dimensional space, and its energy barrier to escape is not influenced by a tensile force, but the microstates that could lead to dissociation are changed by the tensile force; rupture happens along the tensile force direction. An applied force effectively lowers the energy barrier to escape along the loading direction. The lifetime of the biological bond, due to the two concurrent off rates, may grow with increasing tensile force to a moderate amount and then decrease with further increasing load. We hypothesize that a catch-to-slip bond transition is a generic feature in biological bonds. The model also predicts that catch bonds in a more flexible molecular structure have longer lifetimes and need less force to be fully activated.