In the Gae-baek pattern, the 7th and 25th movements use the hands held to the side in pushing motion. What is the practical application of this movement since it does not seem to fit in with the movements made before and after it?
Since schools and organizations that use the Chang-hon pattern set have many variations of the movements and how they are performed, it is difficult to interpret their intention of a movement. Your instructor should have more insight as to the school's interpretation of movements.
The movement in question a slow pressing block to the side using arc hands. As to its practical application, there is none. In a self-defense situation, one would never use a slow block since it would not be effective. Although, it may be used as a posture to show the attacker you are prepared and determined to defend.
Patterns are supposedly imaginary fights against multiple opponents. Therefore, sometimes blocks and attacks are performed toward different directions. This means that, while a sequence of movements may not seem rational when used against one opponent, the movements make sense when used against multiple opponents. Also, patterns have little practical application anyway.
As you know, attacks come fast and furious so there is little time to perform traditional blocking techniques. In a fight, you keep your guard up, go with the flow, maybe block if the opponent is using single technique attacks or the attacks are slow, and take advantage of any openings the attacker presents to attack and finish the fight.
It is practically impossible to fight more than one opponent, except in preplanned demonstrations. Think about the difficulty in sparring one opponent. Now think about having to also spar another opponent directly behind you who attacks simultaneity with the first opponent (real attackers will not take turns attacking). When concentrating on one opponent, you have no idea as to what is happening behind you. The best you can do try to maneuver so both opponents are in view, and then try to eliminate one opponent with a deadly attack so you only have one opponent to fight.
If one persons attacks, you have a choice as to whether to stop, injure, or kill the person. Which option you choose depends on the intent and actions of the attacker. If two persons attack, at the first opportunity you must eliminate one of the attackers. The one you choose may not have intended to seriously harm you, but that's too bad. One opponent must be eliminated quickly and it will usually be the weakest one.
Think about a pattern as a dance routine that is performed using power, perfect movements, and some artistic expression. Pattern practice will make you a better martial artist, not because of the sequence of movements used or their practical applications, but because of the balance, control, perfection of techniques, concentration, etc. that is learned, Good pattern performers are usually good at sparring, since the skills learned in pattern performance help when sparring. However, people who are good at sparring are not necessarily good pattern performers since the skills learned in sparring do not directly translate into better pattern performance.