You have to look at the landings at Gallipolli in the context of Allied war aims with respect to the Ottoman Empire. The Allies were trying to secure a route for supplies to flow from Britain, France and Italy to Russia. The simplest, most efficient way to do this was to get a shipping route into a Russian port. In contrast to WW2, Archangel and Murmansk were underdeveloped as ports, and couldn't be used. St Petersburg was not an option, as the Germans controlled the sea lanes into it. Vladivostok could be used, but was at the wrong end of the country. The Black Sea ports were ideally placed, open all year round, and well connected by rail. The only problem was the Ottoman Empire. Not wanting to divert too many troops from the European theatres, the British and French believed that a naval campaign against the Ottoman Empire was possible. This would involve a combined Anglo-French fleet bombarding the forts of the Dardanelles into submission, steaming through the straits into the Sea of Marmora, and directly threatening Istanbul.

The naval campaign against the Dardanelles forts began on the 19th February 1915, with a major bombardment of the forts at the mouth of the straits. Weather forced a delay until the 25th, when the forts at the mouth were silenced by a combination of naval gunfire and demolition parties of Royal Marines. Attempts at forcing the straits using naval forces continued, with occasional delays from the weather until the 18th of March. Marines were again landed at the outer forts on the 4th of March, but were beaten off by the Ottomans, who had used the delays to strengthen their defences. On the 18th of March, Ottoman mines sank three Allied battleships, and damaged the battlecruiser Inflexible. These losses forced the Allies to change their plans, as it became clear that naval operations inside the straits would be impossible without the destruction of the forts - these were preventing minesweepers from clearing any mines, but the battleships couldn't destroy the forts without the minesweepers clearing the mines. Hence, troops had to be landed on the Gallipoli peninsula to destroy the forts and coastal defences covering the minefields.

T. E. Lawrence (Lawrence of Arabia) advocated for an invasion at Alexandretta pretty early in the war. Having spent considerable time in the region before the war, he recognized that the local Arab and Levantine population had no love for the Ottomans. The Ottoman military also requisitioned supplies and drafted troops from the region, which increased local discontent.

Alexandretta was poorly defended, and was a crucial rail link to all of Ottoman Syria, Palestine and Arabia. According to Lawrence, an invasion there would have cut off those territories from Anatolia, and the British forces in Egypt could have quickly rolled them up without the threat of Ottoman reinforcements. His plan also involved Arab insurrection to aid the British efforts, with the promise of independence if they sided with the British.

The possible landing at Alexandretta was ultimately blocked for political reasons, not strategic. The British and French had their own plans for the Middle East after the war, which did not involve Arab independence. France was promised future ownership of Syria, so they insisted on being a part of any invasion in the region. However France did not commit any troops to the invasion force, so an invasion into Syria was thus off the table. So Britain could not make use of its French or Arab allies, and after failing to make headway through Sinai, they opted to strike towards Istanbul directly to go for a quick knockout, instead of systematically dismantling the Ottoman Empire.

The source for this is the recent book Lawrence in Arabia by Scott Anderson, which is a great read.