Why do you have to be undressed during a massage?

Clothing absorbs the oils used during the session. That's ONE good reason towels were invented.
Not all forms of massage require you to remove your clothing. Shiatsu, a form of Japanese massage, rarely require the recipient to remove their clothing. Other forms just as chair massage, Thai massage, and Reflexology also do not require you to remove your clothing.

The most common form of massage, Swedish massage, does require the recipient to remove clothing so that skin to skin contact can be established. This also gives the Massage Therapist the ability to feel muscle tension, see the body and skin for signs of distress, and feeling of oil or lotion being rubbed into the skin can be very enjoyable.

Today's Massage Therapists, at least the good ones, are trained to do professional draping, which means you change and lie down on the table before the massage therapist enters the room, and you pull a sheet or blanket over you. The therapist will uncover one area of the body at a time, tucking of folding the sheet out of the way as they go along.

If you have concerns about draping or being too exposed, simply express your concerns to the therapist.