Hi there,

It is very difficult to answer counterfactuals or 'why not' questions in history. But I will try my best!

There are several important factors to consider here. These are the Turkish foreign policy at the time, internal structure of the country, and specific factors about those ideologies reception in Turkey.

First, during the Early Republic, Turkey followed a policy of peace where they tried to keep all great power struggles out of their zone (Balkans and the Middle East to the extent that it was possible). A key component of this policy was being in good terms with all major powers. Turkey's relationships with the USSR were impeccable until around 1935-36, despite common crackdowns on the local Turkish Communist Party. With Italy, it was a more complex matter, though things were quite good until the invasion of Ethiopia by Italians, which led Turks to think once more that Italy's imperialist goals may well include Turkey. With Nazi Germany, to the end of the War, the relationships were also quite good. In short, a delicate game of balance to avoid being drawn into open conflict. Clearly, for such a thing to work, Turkey had to stay away from being too closely aligned with one ideology. Being liberal-capitalist would mean an alignment with the British, Americans, and the French. So fascism would be pro-Italy, communism pro-USSR, racism pro-Germany, and so on.

However, it was not as if İsmet İnönü, the leader of Turkey at the time, wanted the country to go towards one of these directions anyway. Granted, to fascism and perhaps socialism they did at times come close. From the time of Atatürk, there were certain laws and institutions selectively imported from fascism, and Soviet help was sought in setting up factories and creating developmental plans. Yet, the goal of Turkey under Kemalism was always, as they saw it, 'reaching the level of contemporary civilisations', which was best exemplified by the West. Closely related to this goal were their Turkish nationalism and the belief that national cultures in this Western civilisation could and would differ. So an Italian could well be a fascist but another country, they believed, could not copy and paste it. Turkey had to create its own plans, its own ideology for its future and this was Kemalism. They could draw inspiration from how the fascists propagated their success and 'educated' their people, they could even think a given ideology was indeed appropriate to their circumstances. So you have Recep Peker, a prominent figure of the Republican People's Party under Atatürk and İnönü alike, writing in his book İnkılap Dersleri [Lectures on the Revolution] that Italy nearly fell prey to communism due to the weakness of liberalism and fascism pretty much saved the country. The same Peker, despite offering to transfer some ideas and 'technologies' from Italy, would argue against others who proposed Turkey to become more fascist, more socialist, more liberal (and so on): Turkey was and had to be Kemalist.

Finally, specific factors. Communism was not an option because, well, the goal was the Western civilisation. Though the leaders of the Turkish War of Independence flirted (some sincerely, some to obtain Soviet support it seems) with communism mixed with Islamism and anti-imperialism/anti-Westernism in the aftermath of WWI, they were never communists. To the contrary, they were determined to suppress the Turkish Communist Party at all times. Also, most countries that became communist in/after WW2 became so thanks to the Red Army. Turkey was not part of the War and therefore the Red Army entering first to liberate the country from Nazis and then to help establish a socialist/communist rule was impossible.

As for socialism, again, partly the lack of Red Army. Also, in Turkey at the time, neither there was a very strong workers' movement (like Italy in the aftermath of WWI, for instance), nor a strong and organised socialist group/intellectuals. So with the ruling party also not infatuated with it (though it was not wholly against left-wing policies in the economy at times), Turkey did not become socialist.

Fascism. Most countries that became 'fascists' were revisionists in foreign policy like Hungary who were left after WWI with hurt or unsatisfied national aspirations. Consider Italy and the prevalent view at the time that WWI was a mutilated victory (vittoria mutilata), a sort of pyrrhic victory for Italy. Some of these also had strong left-wing groups active in the country, which 'fascists' then suppressed. Turkey had none of these. To be sure, it could have them. It was entirely possible for the Turkish leadership to contemplate taking bits of Greece and the Middle East through an alliance with the Germans, for example. However, the wounds and disappointments of WWI were still too fresh for people like İnönü. Most Kemalists, including Atatürk, also thought that adventures in foreign policy were often harmful to internal reform and wealth. As they aimed to transform the Turkish nation, they were not much attracted to the idea of retaking the old imperial lands. Though, of course, with places like Hatay (the Sanjak of Alexandretta then, as part of the French Mandate of Syria, now Turkey) with significant Turkish populations. There, they made a treaty with the French and took it through peaceful means.

The last part of the fascism bit probably responds to your question on nationalism. Turkey was not revisionist because they got most of the Turkish-majority land they wanted after the successful Turkish War of Independence. Hungary did not have a comparable war at the time, for instance, and suffered the Treaty of Trianon as an imposition, and hence it was easier for them to join the Axis and become 'fascist'. Strictly speaking, of course, to say Turkey during WW2 was not nationalist would be false: Turkey was Turkish nationalist then. But with nationalism, I believe, you mean not being a nationalist of a given country and promoting a patriotic atmosphere at home and so on but following an irredentist foreign policy. And this Turkey did not really have except for exceptions like Hatay, for reasons mentioned above.

Hopefully, this will be helpful!