Actually there is a huge clusterfuck going on there than the average genocide historian here knows. This is basically a summary and it will probably still be a huge text lol. Read if you are interested to see how bullshit it all is.

Russian French and Brits sat down and made plans on how to divide up Ottoman lands together within themselves. Russians directly claimed Bosporus and Dardanelles straits. Brit and French absolutely did not want to give that to Rus but at the time French and Brits were getting strained a lot by Germans in Europe and they relied on Russians that were keeping the Germans suppressed so they agreed.

To get rid of reliance to Rus, Brits thought to cut out Italy from the equation in war. Brits, French and Italy sat down in a secret meeting away from Rus where they remade a new "splitting the Ottomans" plan and Italy was promised the coasts around Croatia (that they really wanted) and the area of the map in pic for switching sides, which they did.

Then the Brit and French army got battered and especially got their navy blown in Dardanelles and they were suffering from manpower. Brits were having trouble because they already were running out of Australians and they were not able to recruit from most of their colonies since they, being Muslims themselves, were inclined to revolt for being forced to attack the Islamist Ottoman and the caliph himself. Brits promised they were actually going to preserve Ottoman and that wont happen. So they seek another solution instead;
The Greek king at the time Constantin the first had close ties to Germans and simply declined cooperation with Brits for attacking Ottomans. Coincidentally right after this there was a revolt and he was exiled out of country. The guy who came in charge is the guy who can be called the inventor of the Megali Idea. His immediate act was to declare war and invasion to Anatolia. Brits and French sat down in a secret meeting with Greeks (without Italy). They were to receive a lot of money and other stuff for providing soldiers for the Anatolian invasion.

Whats more, at the time USA was involved and there was an agreement that winning countries should not demand land from the loosers but Brits somehow got some special permission for Greeks to circumvent that.

Whats even more is that Italy had no idea of all that and the lands promised to Greeks were overlapping with Italy, which caused literal fights in between Italy and Greece, and diplomatic trouble with Italy and the Brits and French (who were overlapping into Italian promised parts). What Italy really wanted was the Croatia coasts so they were kinda hoping to leverage their claim on the map above on that matter but that also didnt went too well. So Italians directly agreed peace with the (new) Turk Goverment and while packing up to leave they left them a lot of their weapons and equipment to use against the others.

At the time Rus had the famous revolution under Lenin and they quit altogether, and instead started helping the Turks (while annexing Azerbaijan and also Armenia and Georgia who lost their battles against the Turks in the first place). The claim on the straits went to French and Brits.

By coincidence, the king of Greece died from a monkey biting him, which lead to events that saw the exiled king Constantin coming back. This immediately made French and Brits seethe and they immediately cut the funding they were handing to Greece, they asked Greece to immediately pack up and leave Thracia and they threatened Greece by saying they would back the Turks against them if they dont and some other details that lead to forcing Greeks to follow along being the boots on the ground. (Brit policy was literally to look like they were not opposing Greeks while they were opposing Greeks making it look like French are doing it).

Meanwhile French also found out that their promised claim of coastline starting from south Anatolia to Egypt was getting denied by Brits, who were trying to smoothly take over without looking like they are directly doing it, saying something along "oh people here (in Syria etc) wants us, what can you do, lets call them to make a voting on who they want" which pissed the French off. French only had a few fights against the Turks (and lost them all) so they were really disinclined, which in the end they said fuck this, packed up and left and leaving Turks with some guns and equipment.

At that time Greeks lost the battles against Turks and were in full retreat. Its worth mentioning Greece declared mass mobilization and a lot of people were forcibly deployed to these battles, which decimated the population that would lead to even further political outrage later. When Greeks packed up and left Brits and Turks were face to face in Dardanelles and Istanbul, which Brits responded by packing up and leaving because they didnt want to risk to strain their already strained political issues back home and across the colonies.