Two reasons: to increase literacy by simplifying the language, and to cut ties with the past (ie. the Ottomans) and forge a new secular Turkish identity.
The Ottoman Turkish alphabet, a variant of Arabic, was not well suited to Turkish words and phonemes making it very hard to learn and use. In particular, Turkish has eight vowels, but vowels in Arabic are complicated producing a poor sound-letter correspondence.
This was fine during the Ottoman Empire when literacy was considered something for the elite, not the common people. The new Turkish Republic wanted to improve the lives of the common person, and so literacy was very important.
In Arabic, vowels are often simply dropped from the written language, where as the Latin alphabet is a good match with Turkish vowels. For example <كورك> /kwrk/ has implied vowles. It can be read as /gevrek/ 'biscuit', /kyrk/ 'fur', /kyrek/ 'shovel', /kœryk/ 'bellows', /gœrek/ 'view', which in modern Turkish are written gevrek, kürk, kürek, körük, and görek.
The second, and primary, reason is politically motivated. The Turkish Republic wanted to cut ties with the Ottoman past and create a sense of Turkish nationalism. By replacing the old script with a new one did that handily. By choosing a Latin script the new Republic deliberately weakened its ties with the Arabic world and moved closer to the secular West.
"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."
-- Mustafa İsmet İnönü, 2nd president of Turkey
"Atatürk imposed the mandatory Latin alphabet in order to promote the national awareness of the Turks against a wider Muslim identity. It is also imperative to add that he hoped to relate Turkish nationalism to the modern civilization of Western Europe, which embraced the Latin alphabet."
-- Şerif Mardin
This, combined with the effort to remove Arabic and Persian loan words from the language, "was slamming a door on the past as well as opening a door to the future". (Bernard Lewis).
Unfortunately instead of the five years recommended to make the change over, Atatürk ordered it done in three months which is barely time to make and distribute new materials let alone retrain a whole nation. To emphasize the point, "Law on the Adoption and Implementation of the Turkish Alphabet" (Türk Harflerİnİn Kabul Ve Tatbİkİ Hakkinda Kanun
) meant that all public communications would be done in the new language whether the public knew it or not.
As to why they picked Germany as a model, I can only speculate. Despite losing WWI, Turkey still had strong economic, political, and social ties with Germany and Austria. They shared advisers, teachers, commanders, arms, and equipment.
In contrast the victories Allies occupied Turkey and attempted to carve it up. Just six years before their language reform, the The Turkish Nationalist Movement fought a war of independence against the Sultan and the occupying Allies. They're not likely to be cooperating with them.