Hi Erdem,
In this scenario, please check whether you have been assigned the Office 365 Business license as the following screenshot shows. In fact, if we haven’t be assigned this license, there is no an Office section when going to gear> Office 365 settings>software. So we cannot download Office 2013 suit and Outlook for Mac.
Therefore, if you are not the admin, please contact your admin to check the licenses for you by referring to: Assign or remove licenses, or view a list of unlicensed users.
Please post back if you have the license so that I can look into the issue deeply.
Thanks,
Iris He