Maty Ezraty's reply:
Many teachers, new and experienced, share your dilemma. Learning to mirror your class is an important skill that will improve with time and practice. I heard one clever solution from a wonderful teacher: She would write the letter "L" on the top of her right foot and the letter "R" on the top of her left foot. She would do the same with her hands, putting the opposite letter on each palm and top. This way, all she needed to do was either glance at her foot or look at her hand.
Eventually you can train yourself to see which side is their right and which side is their left just by looking at your students. Until then, you may want to name the walls in your mind, one wall as "right" and the other "left." Whenever you instruct your students to move in the direction of either wall, you will know what to say. Try this until using the right words becomes second nature.
At the heart of your question lies a more important challenge for teachers: teaching from what you see. In order to develop this ability, you have to look at your students. After observing them doing their poses, you can determine what you need to teach that day, for that group. This is the true art of teaching yoga and is the sign of a seasoned teacher. It is also what separates yoga from mere exercise. This ability cannot be honed if you practice the poses with your students or take them into the poses with your back to them. Often it is the way the student has set up the pose that determines if the final pose will be correct or incorrect. This is just one example of what you miss when you teach with your back to your class.
Let me add that there are two general types of demonstrations. In one, you mirror your class and take them into the pose. In the other, more instructional and effective, demonstration, you have the class watch you do the pose, possibly showing them an aspect that you want them to work on.
To summarize, my advice is to demonstrate poses by mirroring them, then come out of the poses in a safe manner to demonstrate how your students should do it. Then step to the side and teach the pose as you walk around the class. Look at your students from all sides. This is how you begin to train your eyes to look, and then learn to teach from your observations. Until you have developed this skill, you are merely exercising your class, and they are following. Teaching yoga is far more than that.