Why does Stack Overflow scan your resume for viruses?

Yes, because there are ways to trigger a malware install or Viruses using a PDF files.

Example:

* https://www.welivesecurity.com/2018/05/15/tale-two-zero-days... (a remote-code execution vulnerability in Adobe Reader and a privilege escalation vulnerability in Microsoft Windows triggered via PDF)

* https://blogs.quickheal.com/beware-pdf-attachments-launching... (PDF's launching Android Malware)

* https://www.sans.org/security-resources/malwarefaq/pdf-overv... (A slightly dated FAQ on PDF Malware)

Any file uploaded should be scanned especially when you are uploading something which is then downloadable by someone else such as this example.

PDFs have been a major malware vector.