A few reasons, depending on what period we're talking about, what is the weapon disposition etc.

First is ration of stabbing. The force that is the encircler is on the outside side of a circle, which is bigger, and can therefore put more men on it than the encirclee. This results in one soldier on the receiving end having to fight, let's say, 1.3 enemy soldiers on average (as a ballpark, not sure about actual numbers, and they vary based on many variables).

Next is flanking shots. If your battle line is curved too much, then enemy on one side of it can shoot into the flank of the troops on the far side, troops who can't use their shields or even see the attack coming since they are busy with their front. This is possible even with melee weapons like spears if the curve is bug enough, or number of men small enough. Warbows and other missile weapons have been often used to fire like this into a fight (from a position that made it impossible or very hard to directly assault them), from what is basically point blank range, for a large number of examples, see Hussite wars (it's what those war wagons were for).

Being encircled also denies you the opportunity to launch flanking maneuvers of your own, and stops you from denying area, allowing the enemy cavalry or archers to maneuver into a position where they get flanking shots or crossfire on you.

Psychological side also has to be considered, it's very, very scary to be surrounded on all sides.

For melee fighting, there's the press. If your formation gets too compressed and lines collapse into themselves, you may well end up in a situation where you can't move properly. If you ever were in a bus filled to the brim with people, you have some idea what it's like. It's even possible to be crushed by the pressure of the crowd itself, as some examples of people panicking in modern times show us, but there are no accounts of this actually happening that I can think of.

Last thing I can think of is that replacing casualties is harder once your lines get all bent - if outer circle has 200 men and second line can only take 180, you need to start pulling in people from the third line eventually in places (and have to put those 20 men from second somewhere), and all kinds of chaos start.

Okay, there are two factors we need to bring up here.

• Pincer movements in general

• Cannae specifically

Let's start with pincer movements (or double envelopments). This is still in essence the most dangerous maneuver to be caught in for a unit for several reasons. Your strategic options are limited. You can no longer withdraw or be reinforced. Your tactical options are usually severel restricted too and become more so as the encirclement is tightened.

Psychologically being surrounded is a bad thing, there are litterally enemies all around. This creates a whole host of problems, you can no longer maneuver effectively to for example reinforce threatened areas, you have no safe place to retreat to rest or care for the wounded, your access to supplies is limited or completely cut off. Lots of really bad things.

If you are caught in an encirclement one of two things usually happens:

• The unit is effectively destroyed, either due to catastrophic losses, such as at Cannae, or due to psychological factors (i.e. surrender such as at Białystok–Minsk).
• A pocket of resistance forms and attempts to hold out awaiting reinforcements or an external force breaking the encirclement. The siege of Bastonge or Hube's Pocket are both examples of this.

So why was Cannae so disastrous? Well, it comes down to a few basic factors. First of all the romans were predictable. They knew they had numbers and attempted to win decisively by breaking the carthagian center. They attempted to do this by forming up in depth and gradually reinforcing an already strong center.

Since Hannibal allowed this while keeping his flanks relatively "passive" the concentration of troops gradually increased in the center. Why the flanks finally pushed in and the cavalry attacked the roman rear the press of bodies in the center became catastrophic. The roman units could no longer maneuver and the invidividual soldiers no longer fight effectively. With discipline/morale failing soldiers tried to get away from the slaughter, pushing further and further into the center which just compounds the problem further.

Only two years prior a roman army under Tiberius escaped (in part) a similiar double envelopment. Varro and Paullus were aware of this and probably felt safe at the open fields of Cannae where Hannibal could not hide any forces or lure them into an ambush. The mistake was, at least to a large degree, their attempt to concentrate forces in the center to break the carthagian line.

Had they not insisted on pushing so hard in the center (or Hannibal not anticipated just such a move) they might have been able to repeat Tiberius' maneuver of forming an open square and fighting their way out. As it was the noose was already too tight when the need for such a strategy became apparent and no space to form an open square existed.

To answer the implicit question here, the romans did not lose at Cannae because individual soldiers were attacked from the side due to flanking troops, they lose because their entire army was funneled into too small an area where they could neither maneuver nor fight effectively. Hannibal turned Roman numerical superiority into a weakness.