Hi Rebecka,
I replicated the issue at my end & was able to successfully print the highlighted text. Please choose the " Document & Markups " option in the print dialog box.
If it doesn't work please follow the steps in this KB doc. https://helpx.adobe.com/acrobat/kb/print-comments-acrobat-reader.html
Let me know if the issue persists.
Regards,
Aadesh