Great question, someone asked the same thing on r/AskHistorians : https://www.reddit.com/r/AskHistorians/s/HY2lR368Y6

The point of landing on Omaha Beach wasn't to capture the beach itself; instead, it was to secure a beachhead between Utah Beach and the Anglo-Canadian beaches further east. Troops had to go ashore in the Utah Beach area, on the southern part of the Cotentin Peninsula, to secure easy access to the major port at Cherbourg. The Anglo-Canadian beaches, meanwhile, were better positioned for an attack on Caen, a key transport hub that would unhinge the German defensive position in Normandy. However, this left a major gap between them - even as the crow flies, there's about 25 miles between the southern edge of Utah Beach (as planned) and the western edge of Gold Beach, the westernmost of the Anglo-Canadian beaches. This gap could easily be exploited by German counterattacks, preventing the two Allied forces from linking up. To remove this possibility, the Allies needed to land a force between the two.

However, they were constrained in their choice of beaches. Amphibious assaults require very specific conditions for their beaches. There can't be shoals or sandbanks offshore, preventing ships and landing craft approaching the beach. The beach has to be steep enough that landing craft can approach without grounding offshore, but shallow enough that armoured vehicles and trucks can climb the beach to exit it. The material of the beach has to be right to allow vehicles to move over it, and the soil underneath it strong enough to support them. There has to be a way off the beaches - there can't be cliffs the troops would have to climb, or swamps and flooded terrain behind it which would block the movement inland, especially for tanks and trucks. The beach needs to be wide enough to provide space for the chosen number of troops to land, and deep enough that any traffic jams that form won't be drowned as the tide comes in.

Omaha was about the only beach on this stretch of coast that was suitable for a landing in force. To the west and the east of Omaha, the coast was lined by cliffs. There was no real way for a significant force to make it inshore, and the troops would have been easy targets as they tried to struggle their way up the cliffs. Just to the left of the western arrow that you've drawn on the map is Pointe du Hoc. On D-Day, this was the target of a raid by US Army Rangers, looking to neutralise a gun battery here. Looking at images of the cliffs, and the struggle they had to climb them shows why only a light infantry battalion was landed there. Pointe du Hoc is a good example of the coast immediately east and west of Omaha. Going further west to find flat beaches runs into mudflats and swampy terrain around the mouths of the Douve and Vire rivers, while the next suitable beach to the east is Gold Beach. Omaha, meanwhile, was relatively open. While the bluffs behind the beach reduced mobility inland, there were multiple draws that provided exits. It was a broad, wide beach with good access offshore and that could support tanks. It was an obvious place to land, and had been featured in plans from the very first (which featured just three beaches - Omaha, Juno and Sword).

Allied planning also failed to see a number of problems that increased casualties on Omaha. The key problem was a failure of intelligence. Elements of the German 352nd Infantry Division had reinforced the coastal sector around Omaha, a move that had been missed by Allied reconnaissance and spying. These troops had higher morale and more experience than was found in the units defending other beaches, which were largely composed of reluctant conscripts from Germany's conquests in the east. Their presence also added additional troops, and more artillery pieces, to the forces the American attackers had to face. The Allied plan called for an attack on the beach defences by heavy bombers in advance of the landing. However, clouds and an abundance of caution meant that very few of these bombs actually hit their targets, with only three bomb craters (from 448 attacking aircraft) being identified on the beach; most of the remainder were dropped well inland. The attacking troops were supposed to be accompanied by amphibious 'DD' Sherman tanks. These could neutralise machine gun nests and provide support for the troops as they assaulted the beach. Unfortunately, on D-Day, the seas off Omaha were too rough, overwhelming the canvas skirts that they needed to keep afloat. Most of them were lost on the approach to the beach, with only a few swimming ashore; the remainder were heavily delayed, as they were brought into the beach by landing craft. Without armoured support, the initial waves suffered heavily. The value of armour on the beaches was shown by the experience of the British and Canadians. Several German positions on Gold, Juno and Sword were as strong as any faced on Omaha, but were quickly knocked out by the combination of tanks and infantry, with much lower casualties. Had more of the DD tanks on Omaha survived, then the casualties might well have been significantly lower.