They knew they were weaker in cavalry, and that's precisely why they accepted battle when it was offered in a confined space (the battlefield at Cannae was flanked by a river on one side and a hill on the other, limiting the width of the battlefield). They seem to have reasoned that if they limited Hannibal's cavalry's ability to outflank them, they would have neutralized his best weapon against them.

So, their plan was essentially hold the flanks, and use their superiority in the center, in infantry, to punch through the Carthaginian center.

In effect, it would have been like a race. Can the Romans break the Carthaginian center first? Or will Hannibal's Numidian and Iberian cavalry defeat the Roman flanks first?

And once Hannibal offered them battle in a battlefield limited in width by geographical features, it would have seemed to the Romans that Hannibal had accepted a significant handicap in how easily and rapidly he could defeat their cavalry.

So, they probably thought they could win the race. Especially given how much they outnumbered Hannibal in infantry, and in infantry quality.

And to make sure the race wouldn't be close, they did a number of things that they thought would help them break the Carthaginian center faster. They packed in their infantry in extra close order, to maximize local numerical superiority. And when they made contact with Hannibal's crescent shaped infantry formation, they crowded in to the center even further, seeking a local breakthrough there, rather than bending around the Carthaginian line to engage it in the entirety.

Hannibal, of course, had foreseen exactly what the Romans would do (truly, one of the finest examples I know of "that day he seemed to be in command of both armies"). So he took a number of measures that delayed, if not out-right defeated, the Romans' plan to break through his center. The crescent-shaped initial formation, the mix of his infantry to carefully control the rate at which the different parts of the outwards crescent line would give ground, and finally, the two phalanxes of Lybo-Phoenician infantry, oriented inwards, to squeeze the Roman infantry in tight at the last instant, to the point where they no longer had enough space to even swing their swords, arresting their advance.

Source: Probably the first book I read on this was Theodore Amyrault Dodge's, which I first read... good grief, so long ago. Boy do I feel old now.

Edit: btw, What Hannibal pulled off at Cannae is termed a "double envelopment." Pincer movement is a term more used with maneuver/operational warfare. E.g. what the Mongols did in the lead up to the battle of Mohi Heath. Or what the Germans were attempting at Kursk.

The strategy was to punch through Hannibal's center with the Roman's numbers and weight, hopefully quick enough that the Carthaginian cavalry wouldn't have time to respond because they were tied up with the Roman cavalry. Presumably, if the Romans were able to achieve a quick breakthrough, they would be able to circle back and envelop both flanks of the Carthaginian foot. The Romans had some success breaking through the center at Trebia, and wanted to repeat the feat but actually win (which the extra numbers would ensure).

Now, obviously this didn't work out. Their line could have been extended, but was limited on one flank by the Aufidis River. The Romans had suffered heavy losses and presumably the Roman troops were not experienced. One of the best ways to reinforce morale is to make sure your troops can't run away because there are a lot of troops right behind them. It's also possible that such an inexperienced army wouldn't be capable of any but the most basic of maneuvers.

Now, we can look back and criticize Varro, but it would be an exercise in futility.

Both of the posts so far are quite good and I dont disagree on the general idea. But I would suggest that a lot of problem with recreating these battles of the Punic wars is that they are often described to us in terms of parade ground maneuvers and it seems a lot of the tactical details have been left out.

If you look at accounts of Metaurus River, Ilipa, or Trebbia they are all quite hard to imagine working because the description seems so abstract. At Ilipa we are told of Scipios velites sort of fanning outward in some sort of mix of columns that wrap around the flanks of Hasdrubal's army. Its hard to imagine how that really worked.

Or at Metaurus, they have Nero's division on the right, simply disengage and march across the rear of their own army and land on the enemy's left whereas the Gauls they faced just sit their and do nothing. it is quite hard to imagine. But if that battle was more of a running battle, let's say, and these divisions were engaging Hasdrubals forces as a column in retreat. Well it may make more sense if Nero had put to flight one part of a column and then moved up the road to join in another battle already going on. Some sort of practical consideration must have caused the battle to turn out the way it did; it just doesnt seem to make sense as an abstract idea of him disengaging and marching across the rear like that.

So the battle comes down to us related in rather simple terms about this convex line and Hannibals forces simply overlap it and turn inward. It all seems so simple. I suggest that there must be lots of details that are missing from these accounts, that we will never really understand how they were able to pull it off the way they did.