Don't let the title fool you, I don't mean training on your days off.
I am referring to those days when you're just not at 100% or you don't "quite have it".
After having trained myself, and trained other people for several decades (between martial arts, military, & fitness) I have seen several patterns that continual arise.
What we're discussing today is one of them.
People that train consistently and train hard will have those days when they are feeling weaker, slower, or just kind of sluggish. Sometimes that will keep them from training.
If they are injured or are on the verge of over-training, then they should take some time off. Aside from that, most often they will benefit from working out anyway, in spite of how they feel.
Feeling are elusive and unpredictable, they should not dictate your training schedule to you.
Remember who's in charge: You are!
It's your responsibility to rise to the challenge in front of you and to strive for excellence.
That is the mark of a seasoned athlete; and it is the mark of a mature & experienced trainer/coach if you expect that from those you train.
When you load that barbell and it feels extra heavy, even though you've trained with at least that much before, you must persist and go for it any way!
You will still benefit from the work you do. Weight training in any form will generate benefits to you even if you're "not really into it" that day.
The world is full of out of shape people who aren't quite motivated enough to workout yet (but they plan on it one day, so they say).
Good athletes can always become better athletes.
You'll notice them because often they are the only person lifting, or running, or practicing their skills. The whole place can be empty except for them, and they don't care. They just do the work.