Please note that if you have a work or school account, you might not have a version of Office that supports co-authoring yet.
Forum Discussion
Not able to have all users be in the same excel file at the same time in Sharepoint
You do not need to use Excel online to co-author, you can use Excel local client or Excel mobile, but it has to be from an Office 365 tenant login. I assume the file is in .xlsx format? So the issue you're asking is that you want users to be able to co-author, but its not and instead users are getting the "file is exclusively locked by X user" message? Is this file stored in a SharePoint document library? How are you opening it? From the library, or from Teams, or other? Give this a glance and see if it helps, it even has a section about the file locked error:
https://support.office.com/en-us/article/collaborate-on-excel-workbooks-at-the-same-time-with-co-authoring-7152aa8b-b791-414c-a3bb-3024e46fb104
There are constraints though: https://support.office.com/en-us/article/collaborate-on-excel-workbooks-at-the-same-time-with-co-authoring-7152aa8b-b791-414c-a3bb-3024e46fb104Collaborate on Excel workbooks at the same time with co-authoring - Office Support