There were already discussions of a new alphabet system because the Arabic alphabet had problems codifying the palace language (Ottoman Turkish) and wasn't really formalized to fit the standard rural Turkish before Atatürk too. Details of the inconsistency would be better explained by a linguist, but it was heavily discussed that the alphabet didn't fit the language. There were several attempts at promoting the Latin alphabet during the 1910s. Enver Paşa even invented a brand new writing system based on the Arabic alphabet called Huruf-u Munfasıla and tried to get the army to adopt it, but it fell out of favor quickly due to its impracticality.

There were alternatives to the Latin alphabet like adapting the Arabic alphabet, adopting an old Turkic alphabet or creating a new one but these proposals were rejected because Atatürk envisioned a Western oriented Turkey, and adopting the Latin alphabet emphasized that goal.

Literacy rates in the late Ottoman empire were really low, estimated between 6-10% before the revolution and most of the literate population were the educated elite, state bureaucrats and officers in the army. A very large percentage of those were already literate in French and/or German due to Westernization efforts of the late Ottoman administrations, therefore familiar with the Latin alphabet. Some discussions about it make it seem like a huge reform that shook the foundations of the culture, but in reality it was relatively easy to adopt and massively successful too, as indicated in literacy boom of the young republic between 1923-1938.

Şakir Ülkütaşır, Atatürk ve Harf Devrimi

Harf Devriminin 20. Yılı Sempozyumu, TTV

"The cornerstone of education is an easy system of reading and writing. The key to this is the new Turkish alphabet based on the latin script." - Ataturk

"The alphabet reform cannot be attributed to ease of reading and writing. That was the motive of Enver Pasha. For us, the big impact and the benefit of alphabet reform was that it eased the way to cultural reform. We inevitably lost our connection with Arabic culture." İsmet İnönü (second President of Turkey)

This must be seen under the context of expanding the secularization of the society, that is, making people accept a full separation of the state and religion, which was otherwise a common trait of the Middle East politics (even to our days). Another language-related measure was the creation of the Turkish Language Association (Türk Dil Kurumu, TDK), which was in charge of creating an official dictionary for the language, among other language-related measures, including removing as many loanwords of Arabic and Persian origin from the Turkish language as possible. This was one of the highest priorities of Ataturk, for example he went against the advise of the Language Commission of doing the alphabet transition in 5 years and he ordered for it to be made in 3 months.

By all means Ataturk shouldn't be seen as the sole revolutionary mind behind those pro-western views. The Ottoman administrative and military (and the small middle) class was already getting used to the western intellectual tradition since the early 18th century through the Ottoman-French alliance, starting with the Tulip Period, a process which would fasten after the French Revolution (we should remember Napoleon invaded Ottoman-owned Egypt), specially through the subsequent invasions from a more modernized Egypt against the Ottomans, which would take direct British Naval prowess through the Nile River to stop.

Those episodes and previous developments helped the pro-reforms sectors of the governing class to successfully begin implementing western-based reforms in a process named the Reorganization (Tanzimat), which would end with the brief First Constitutional Era (1876-1878) and subsequent reform regression/stagnation made by Sultan Abdul Hamid II. But that the Sultan halted those progressed didn't mean the administrate/military/middle class halted their movement toward pro-modernizing feelings, this would ultimately culminate in the Young Turks Revolution in 1908 and the start of the Second Constitutional Era.

Ideas for changing the alphabet would begin by then, since the Perso-Arabic alphabet works poorly for the Turkish Language due to the lack of vowels, meanwhile in Turkish, with their common usage of small words and names, usually distinguished words by adding more vowel variety than most languages. During the Ottoman Era this was partially patched through increased usage of Arabic and Persian loanwords for any confusion-prone word (unless heavy ambiguity was desired), but the non-elite was hardly accustomed to that usage of the language, which proved difficult for the Young Turks to deal with in their state expansion ideals. Multiple reformations to the Perso-Arabic Alphabet were suggested, but none ultimately gained enough support or traction and the issue (since it was considered an issue by most the intellectual community) was left unresolved and a solution delayed.

Now, the idea between reforming the Perso-Arabic alphabet or adopting the Latin alphabet (and modify to Turkish needs as well, which was a much easier process) ended up becoming a pro-Ottoman/Religious vs pro-Turkish/Secular identity (since a script change also produces a disconnection with previous writings, and for religious with the sacred language for the Quoran). The conflict would have continued for some decades most likely if it weren't for the First World War and the Ottoman Defeat, the subsequent Sultan (which was also the religious figurehead) siding with the Greeks colonist and the subsequent Republicans lead by Ataturk which defeated Greeks, English and French and was able to hold most the modern Turkey territory.

Through some expansion was attempted (and to some extent succeeded), everyone knew after the Independence War that expanding the territory much further Turkish lands was not realistic and attempts to shape up a new non-Ottoman identity, the Turkish identity, took priority and any ambiguity elimination with the previous identity was seen as the goal. Any supporter of Ottomanism (and all that it meant, like Sharia Law instead Secularism) was left without any support or power, basically.