agreed with Shytehawk, at most airports it may seem the pushback is a straight line off the stand, but the A/C still needs to be turned to go the correct way down the taxi-way for the runway he/she will be using..
as for the tug leaping forward, to put it in simple terms.. imagine ur pulling a heavy weight on a rope, the rope breaks while your pulling it... u will go flying.. now imagine that reversed when it comes to pushing an aircraft which weighs upwards of 30 tons