What is the definition of catch up with the deer in idiomatic expression?
it means you are not as fast as somebody else
A panther will most likely win over a deer. Even if the deer can fight with its antlers (provided it's a male deer on or near to the rutting season), body muscles and hooves, a panther could dodge it easily since it is fast. One bite on the throat is enough to kill a deer. Panthers routinely catch deer for food.
WHen deer are in the dark say by the side of the road and a car's headlights shine on them, they are blinded momentarily and are susceptible to being shot. That why this method of deer hunting is against the law. It is an experession that means that you are too stunned to move. In other words you are terrified. It comes from when you catch a deer in your headlights and they just freeze.