eli5, In a battle, why being surrounded is such a disaster?

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It seems even if you had bigger numbers, if your army is attacked on multiple sides you lose. Cant soldiers push from a single point strongly to break it? I am thinking of a historic setting, no thecnologically advanced weapons.

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It has to do with the “surface area” of the front lines, compared with their depth.

If an army is surrounded by an army of equal size, the surrounded army is going to start losing space to deploy its people to the front, where melee fighters can actually make a difference. Soldiers standing in the middle of the formation won’t be doing anything, won’t contribute to the battle until they can get to the front, and so may as well not be part of the army. A big blob of soldiers who can’t fight because there isn’t enough space in the lines to deploy them are just a liability.

Meanwhile, the surrounding army has the opposite advantage. All of their ranged attackers will be able to focus their fire in an area with ever more enemies to hit. Lobbing catapult stones at a line a few people deep isn’t going to do much for the defenders, but the attackers get to hit the front lines and also all the people behind them who can’t fit on the front. Meanwhile, at the start of the fight, the surrounding army will be able to deploy all of its melee fighters effectively, only losing area to deploy them after they’ve already pushed the defenders back into a formation easier to pick off from afar.

Historically speaking (WW2), being surrounded meant three things:

1. No communications with higher levels of command. Most communication was done either via field telephone lines (which were obviously cut if surrounded), or via messengers (which were obviously captured if surrounded). With no way of knowing how the general battle is going, no way to call for help, and no way to get orders, most units went on auto-pilot. This went reasonably well for armies trained in that way (e.g. Germany), but very very badly for more hierarichal command structures (e.g. Soviet Union, France).
2. No supply. This is the reall killer. Most armies had enough food, fuel, ammunitions and spare parts to last them about 1-2 days. After that, normal battles are out of the question. Every shot you fire is one less you have for tomorrow. Every drive with your tank means a little less fuel in the tank for tomorrow. And every snack you munch is one less food item in your reserves for tomorrow. That really get to the soldiers, and means that you cease all unnecessary action, i.e. you become passive. That hands over the initiative to the surrounding army, which is half the way to defeat.
3. No extraction for the wounded or killed. This is a morale killer. If a wound gets you a ticket home for a few weeks, soldiers tend to do their jobs much better than if a wound means dying in a foreign swamp unless being captured by a potentially gruesome enemy. Also, all vehicles and heavy weapons damaged while surrounded are lost immediately. There’s no way to get them back to a repair shop. That multiplies the loss rates for heavy equipment tremendously.

Being surrounded means you have restricted access to resources. That makes it difficult to continue fighting, because you can’t restock ammunition, food, etc.

Being surrounded also removes the possibility of reinforcements. Soldiers are people too. They get tired, injured, and otherwise decrease in fighting ability as these things happen. That’s concerning for a battle.

“Pushing from a single point” doesn’t work, because the army that’s surrounding you can attack from behind *and* the side. You can’t push at a single point; that’s one of the primary benefits of surrounding someone.

Interestingly, sun tzu says in art of war to never completely surround your enemy, always give them a break out direction because if they know they are trapped they will fight hard.

One of ceasars great victories in gaul, the battle of alesia, he was surrounding a town and then a relief army showed up and surrounded him. He built like a double fort, one side facing the town he was besieging and one facing the relief force.

Oddly, it’s one of those things that’s always been true, even when warfare changes radically.

Two big points. One, when you have a large number of men in a terrifying and confusing situation like battle, the main thing that keeps effective and keeps them from freaking out and running is strict order/discipline. This tends to mean everyone facing forward and knowing they could pull back if they needed. Two, armies need a constant flow of supplies and communication, which generally comes from behind.

If an army is surrounded, it’s exposed to attack from directions it can’t easily respond to. You can sort of circle up against all sides but that’s a hard maneuver to pull off under constant attack and confusion, and it limits your movement options badly.) Your men tend to panic knowing that they have nowhere to run. In the case of a longer battle/siege, your men will start to get hungry, thirsty, and low on ammunition soon.

To your second question: Yes, it’s called a breakout, and it’s a top priority when you’re encircled! Unfortunately, it’s also risky. Your men will be attacking hard to break through enemy lines, who are comfortably defending. You’ve pulled men away from the main force which is now weaker and still surrounded. Your enemy holds all the cards, and can keep attacking your fleeing men from all sides, or let some escape and then cut them off (now you have two smaller encircled armies!)