During the takeoff the engine is pushed to the max right near the ground, making it one of the most critical phases of flight. Should the engine fail, there is not much time to investigate or think through the best course of action before the airplane hits terra firma. It is therefore a great idea to get as high as possible as soon as possible. And in a retractable airplane, one way to achieve that goal is to get the gear up as soon as practicable.
You may have been taught to wait to retract the gear until you reach the end of the runway, the argument being that you would land on the gear instead of the belly of the airplane should you have an engine failure. But if the engine fails halfway down the runway, you would likely not have time to get back down and get the airplane stopped before the end of the concrete.
Unless you do in fact get the airplane on to the tarmac, an unlikely event unless the runway is extremely long or the engine fails before or right after rotation, you will likely land on a soft surface such as grass, sand, dirt, a rough field or even water depending on the surrounding area. In these cases you are often better off landing with the gear up as the nose gear can dig into the ground causing the airplane to flip over. Remember, in emergency situations your prime focus should be to minimize the injury to yourself, not to minimize the damage to the airplane.
By retracting the gear as soon as you have the indication of a positive rate of climb you will gain critical altitude quicker and give yourself more options in case you have an engine issue. It is highly likely that you would have plenty of time to lower the gear before you hit the ground should you find a suitable, hard surfaced emergency landing spot.
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