Hi JimSatterfield
The announcement in April 2017 gives the best summary of why the decision was made to end support for non-mainstream supported Office client versions connecting to Microsoft 365 services (primarily security related). Though to be clear, Office 2013 client itself is still supported until 2023, it’s the connectivity to Microsoft 365 services that will no longer be supported.
Lastly, Microsoft will not take any active measures to block older Office clients, such as Office 2013 and Office 2010, from connecting to Office 365 services. However, legacy clients attempting to connect to a modern, always up- to- date cloud service may experience performance and reliability issues. Customers will face an increased security risk, and may find themselves out of compliance depending on specific regional or industry requirements. Microsoft Help may not be able to resolve issues that arise due to unsupported service connections.
Thank you for reaching out with your question!
Miriam