Meditation is one of the surest ways to let go of old habits and habitual reactions. As you have discovered, it isn't possible to purify the mind just by thinking about it. A fearful mind cant conquer its own fear, and anger cant quench anger. Meditation is a powerful tool for going beyond the domain where fear, anger, and all forms of emotional toxicity hold sway.
When you meditate, you enter deeper and deeper levels of yourself until you enter the space of pure awareness. The silence of pure awareness is extremely refreshing to the mind, which finds it increasingly easy not to cling to old thought patterns; rigid habits of thinking and feeling begin to fall away of their own accord. Its a kind of letting go, allowing yourself simply to be. Meditation is a gradual process, but as you continue to meditate, your experience of clarity and wellbeing will expand and become the norm, extending out into your life beyond your meditation sessions. As you take your mind back to its source, over and over, it will become free of outmoded patterns and beliefs that no longer serve you.