Not addressing a thought when meditating If I, for example, was meditating, and the thought came in my mind, say, obsessive-compulsively (meaning it keeps resurfacing due to the fact that the thought bothers me): "I'm a bad person", if I ignored it and returned to my breathing, would my not addressing the thought and thinking "No, I'm not, and here's why.." cause me to subconsciously believe I'm a bad person? It's holding me back from meditating because I feel uneasy about dropping the thought.
Obsessive-compulsive tendency means attachment to thoughts, giving them too much importance. Instead of addressing thoughts, we can observe our mind. It's like reflections and mirror. If you are captivated by reflections, or struggle against reflections, you manipulate with reflections - and they remain in power. Instead, you can shift your attention to space where reflections happen. Mirror is not touched by reflections.

So if you just observe the thoughts, not trailing them with more thoughts, not being captured by thoughts, then you can remain in stable mind, untouched by thoughts. Your mind will gradually realize their illusory nature. Thoughts have causes and effects, so they have no power by themselves. All their power is brought by causes and conditions.

Meditating, you can gradually develop awareness of thoughts and their causes, and develop non-attachment to them.

For example, you could realize that "I am a bad person" is just a stupid idea, an illusory construction that has nothing to do in your life.

PS. In case of "constant thinking", the thought repeats again and again. Why does it repeat? Because there is some intention beyond repeating thoughts. Then we can use several methods:

(1) Keep the observation and try to let go of thoughts. Eventually the mind may get bored with that thought and stop repeat it.

See also: Letting go (Ch'an Newsletter - No. 24, September 1982)

(2) Investigate the intention. "Why does this thought return, again and again? What for?" Investigating intentions, you could change your mental processes and get rid of obsessions.

For example, the thought "I'm a bad person" can come due to the intention to understand that marking people as "good" and "bad" is not an efficient way to deal with problems.