My coached athletes always have a day off every week. This is because they are working athletes with jobs and families and they are not being paid to workout. Because working out is a stressor, one day a week is off to give a break both mentally and physically.
That said, a carefully constructed training plan does NOT need a complete day off once a week.
If you are doing active recovery, a session that makes you feel better after counts as better than a day off. For runners, a yoga session, swim or chill bike ride can count as active recovery and be part of a training plan as an off day. Remember though, off days are also important for mental health. Sleeping in can sometimes be just as beneficial as your active recovery.
Your day off or active recovery day doesn't need to be a Monday or a Friday if you work a traditional schedule. Think about which day is best for taking off in the context of your workout flow.
For example, if you generally have two hard days or workouts on Saturday and Sunday, I would NOT choose Monday as a day fully off. I would choose Monday as a day of active recovery, mobility, etc. Tuesday could be a day off and then back to running on Wednesday.
For some people a day off is picked for them because of long work days, family duties or other time limitation. If you have a day off picked for you, make sure to schedule your hard workouts around it if you can.
Want to talk through what day is best for your schedule? Ask at this week's office hours.
Link to Tuesday office hours Zoom meeting here. 7:30-8:30pm