Read Maty Ezraty's response:
It can be very frustrating to receive different instructions about yoga postures. Keep in mind that there are many different ways to practice. Instead of looking for the right answer or the only answer, learn to embrace the different information that is available. Then you will be able to make an educated choice.
In my teacher trainings, I encourage students to notice what they gain by practicing a pose one way verses another. In this way of thinking, we become less dogmatic and more open to learning. Remember that what is right for one student may not be appropriate for another. Also, through our practice we evolve—and sometimes change—our opinions. For example, B.K.S. Iyengar, a master of yoga who still practices at age 89, continuously improves and fine-tunes his teachings, improving the use of props, therapeutic work, and alignment throughout his lifetime.
However, sometimes we must put aside our opinions and trust a seasoned teacher. Experienced teachers whom we respect and trust are important in our yoga path. It may be beneficial to stick with one teacher's approach until you understand it thoroughly.
Balance the practice of listening to your inner voice and following what feels good to you with working with teachers who have been on the path longer than you have. Finding this balance is an art, and it brings truth and humility.
Now, to answer your question more directly, I find many benefits to practicing asanas with the eyes open. In Ashtanga Yoga, we have specific gazes for each pose, which helps bring the mind into the desired state.
In the Iyengar system, the eyes are often open but soft, quiet, and introspective. Some teachers believe that when the eyes are closed, it is easy to lose a sense of what is real. I have even heard some teachers say that closing the eyes may be counterproductive for students who are depressed.
I once read that meditation teacher Rajneesh recommended meditating in a noisy marketplace, because it helps you learn to deal with outside distractions. This idea relates to your question: When the eyes are open, we must be present in the world; the practitioner is both in the world yet deep inside.
This is not to say that the poses can not be more introspective with eyes closed, or that this practice is incorrect. In restorative poses and in some long-held postures, letting the eyes close brings definite benefits, such as drawing the senses inward, calming the facial muscles, and achieving a deeper sense of relaxation.
Remember that more important than finding one answer is to realize the value in all the choices. At first it may be necessary to trust a senior teacher and follow a well-worn path. Practice for a long time. Then teach your truth.
Maty Ezraty has been teaching and practicing yoga since 1985, and she founded the Yoga Works schools in Santa Monica, California. Since the sale of the school in 2003, she has lived in Hawaii with her husband, Chuck Miller. Both senior Ashtanga teachers, they lead workshops, teacher trainings, and retreats worldwide. For more information, visit http://www.chuckandmaty.com.