The way I see it, your hour of yoga class is a place to find peace. The world is full of stress, fear, and all kinds of disturbances. I don't see any need introduce more of that into the yoga class than is already present in our lives.
To that end, I instruct people that their practice should ultimately feel good. Even if they are challenging themselves, there should be some element of ease and pleasure within the challenge. Life will hand us enough struggles. Pushing ourselves on the mat, striving toward some goal of "perfection" in a pose, is completely unnecessary.
Sometimes beginners tell me that they were intimidated by yoga at first, but after my class they felt comfortable.They weren't sure they could "do yoga," but eventually came to understand that yoga is more about the process than a goal.
As a teacher, I give a lot of verbal instructions about how to safely get into a pose, However, this isn't to make students feel as if they have to have every little physical detail perfect, or that they are doing anything "wrong." Rather, it is to help them to focus their mind, and get out of their head and into their embodied experience. My goal is to have students develop an inner focus, and ultimately, become one with their higher selves. That way, they can develop their own organic, inner-focused yoga: they can find their yoga.
This, to me, is the essence of yoga. It is my hope that students come away from my class with a greater sense of ease and empowerment.