Yoga classes are where I learned to see myself through the actual experience of being myself. I felt my resistance to external direction; I recognized deep inner sorrows; I discovered flexibility and habitual patterns. Over time, every bit of this moved off the mat into my daily life, relationships, self definitions. On a grand scale of patterning I was shifting and changing, but the minutia upon which the patterns all relied was discovered only in my personal practice. Allowing the experiences on the mat to go where they led themselves, taking on the challenges of body and mind that arose from my own body and mind. Classes will give you the tools for this, but only the personal practice gives you the opportunity.
An example of this might be a reluctance to kick up into handstand with "the other leg." It is one of those moments in private when you face your drive, your judgment, your fear of failure and the pain of that. You can seek out the mechanisms by which the body can actually support the move, rather than throw the body into the panic again and again until it somehow "works." You can deconstruct and reinvent the pattern in the movement, and without a care about the handstand, discover the rising into it. Feeling pain in class in a joint or in a movement, you will quite simply try to avoid it the next time. In private practice you can explore the sources to support safe movement, or to genuinely protect the point in jeopardy. You can evolve the practice from the foundation into the pose or movement, building the resilience and awareness that bring you fully into the pose rather than aiming for the shape of the asana. Strength and stamina can be built, and the self defined differently.
Meditation practice requires a most intimate connection to solitary practice. In a group of people, meditation puts you directly in touch with your own mind and habits of mind. The group can support you with community, scheduling, breath around you, and a little pressure to keep your seat out of shame or anxiety. A group can even offer you material to work with in the form of distraction and dharma themes upon which to focus your thinking. It is in your own practice where you find the threads with which you have been spinning the stories, and where you can stop that spinning and can observe the threads, and the stories, without having to give over to watching them.