You have to trust this simple ability that we all have to be fully present and fully awake, and begin to recognize the grasping, and the ideas we have taken on about ourselves, about the world around us, about our thoughts and perceptions and feelings. The way of mindfulness is the way of recognizing conditions just as they are. We simply recognize and acknowledge their presence, without blaming them or judging them, without criticizing them or praising them. We allow them to be, both the positive and the negative.
When I started practicing meditation I felt I was somebody who was very confused, and I wanted to get out of this confusion and get rid of my problems and become someone who was a clear thinker and might one day become enlightened. But then, reflecting on this position that “I am somebody who needs to do something,” I began to see it as a created condition — it was an assumption that I had created: “I am somebody who needs to do something in order to become enlightened in the future.” Just by recognizing this as an assumption I created, that which is aware knows it is something created out of ignorance, or not understanding. When we see and recognize this fully, then we stop creating the assumptions. Awareness is not about making value judgments about our thoughts or emotions or actions or speech. Awareness is about knowing these things fully — that they are what they are, at this moment.
Ajahn Sumedho
By not stopping our thoughts and feelings in meditation, we are paving the way for gentle ways of being with our experience. When thoughts are intentionally cut off, that is often an act of harming. If it is done aggressively, even with a miniscule amount of force, it supports and furthers the tendency to get rid of thoughts rather than the tendency to get to know them. Our ability to get to know our thoughts and feelings depends on our ability not to get rid of them. Holding our experience gently, thoughts and feelings come and go in their own time. 
Mindfulbalance 