Istanbul or Konstantiniyye with it's old name - which means City of Konstantin - was the capital of Ottoman Empire from 1453 to the end. It was by far the most developed and populated city of the region and to this day, it still is. So this question is reasonable and it might be hard to understand this decision without knowing the Turkish history and as a Turk myself, I am going to try and explain the reasons.

Ottoman Empire surrendered to Entente, signing the Armistice of Moudros in 30 October 1918. After that point, Istanbul was technically under occupation of Entente powers, however it wasn't official yet. Meanwhile in Anatolia, there were regional resistance movements against Entente occupation.

In 28 January 1920, Ottoman Parliament held it's last meeting and published bunch of decisions known as 'Misak-ı Milli' at 12th of February. Misak-ı Milli is basically a national oath, something similar to Manifest Destiny. I can give more information about that but since it's not our topic right now, I will move forward.

This frustrated the British and caused the official occupation of Istanbul, starting from 15th of March which would last for 3 years. They shut down the parliament and arrested congressmen who couldn't flee the city. Meanwhile, the local resistance movements in Anatolia were now unified under Mustafa Kemal's leadership and he invited the congressmen who could flee to Ankara, along with new representatives from all over the country to form a brand new parliament in Anatolia.

I believe, reasons why Ankara was chosen as the base of the new parliament also explains why it became the capital of newly formed Turkish Republic.

So, why did Mustafa Kemal chose Ankara, a small town? Obviously Istanbul and western parts of Anatolia were not avaiable but there were bigger cities like Sivas, which was the place the congress which united all regional movements were held. There are several reasons:

1. Ankara was in middle of railway systems which made a perfect base for logistical purposes.
2. It was closer to western front which was to decide the outcome of war, compared to other suitable candidates.
3. There were already some members of Ittihad ve Terakki(governing party of The Empire during The Great War and Mustafa Kemal also was a member of them before he left due to disagreements.) and even the building used for first parliament belonged to that party.
4. If you check the map, you can see it's clearly in middle of the country and a good place for government. Today, distances are not really an issue anymore but back then it was important for communication.

Fastforward to end, in 30 August 1922, Turkey has won the Independence War and a year later Istanbul was also liberated from British occupation without a bloodshed.

I guess this is a sufficient answer but in order to let you have a better understanding I will explain why Konstantiniyye was chosen as capital by Ottomans and why wasn't by Turkey.

It was in a central position by the time Mehmed II conquered the city and as he planned to expand forward into Europe, it was also a suitable base for military purposes. Also, it was a trade center and a very prosperous city which made it even better as a capital. Besides all of that, Mehmed II proclaimed himself as The Roman Emperor (Kayzer-i Rum) and he wanted to claim the heritage of Eastern Rome. He then conquered Trabzon as well, to eliminate the last rival to his title.

Republic of Turkey didn't have anything to do with Rome and was more nationalist since that was the new trend of that era. Istanbul was occupied for a long time and it was obviously not safe from any occupations in future. Since Mustafa Kemal Ataturk was afraid of a new world war in future, he tried to prevent another national trauma with the occupation of capital. Another reason is, as you can guess, after the losses in Balkans, Istanbul was no longer in a central position and as a matter of fact it was very vulnerable militarily since it's hard to defend a city so close to frontlines. As an addition to all of these reasons listed above, Ataturk wanted to build a modern European capital to be a model for the new, modern Turkey.

I tried to explain as best and simple as I could and if you have any further question I'd be more than happy to answer. If you want to have a detailed reading, you can read 'The Great Speech' written by Mustafa Kemal Ataturk which covers the Independence War in depth.