You could stain your shirts.

You could get accused of cheating.

It might be a romantic gesture to write a woman's phone number on your arm, but it also looks unprepared.

There are better answers, with two exceptions:

When you get an infection and you don't know if you should see a doctor about it (cellulitis, insect bite), outline the red area with a pen and note the time. If the red spreads bigger in 12 hours, you need to see the doctor.

If you think you're going to die or have taken an overdose, write the meds you took on your arm after calling 911. That way, the EMTs will know what you took.