Why might an ATS read my two-column resume in the wrong order?

Because software extracts text in the order it is stored in the file, which is not always the order your eye follows on the page. A person reads down the main column and then the sidebar; a program may read across the page instead.

When that happens, a line from your skills sidebar can end up joined to a job title, or your contact details can appear in the middle of your work history. The system may then put information in the wrong fields or miss it.

How the template was built matters: tables, text boxes and separately positioned blocks are more likely to cause this. A single column avoids the problem because there is only one sensible order.

You cannot see this from the page itself, because the PDF looks perfect on screen. The only way to check is to extract the text: select all, copy, paste into a plain text editor and read it. If the result reads like your resume from top to bottom, the risk is low. If it reads like two documents shuffled together, use a single-column version for online applications and keep the two-column design for people you contact directly.