Not addressing a thought when meditating

The answer depends on whether you are practicing Samatha or Vipassana meditation. Vipassana meditation has two aspects of knowing and developing. That is Samma Sati (right mindfulness) and Samma Vayama (right effort).

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?

You are over-thinking/analyzing this which tends to result in further thinking. This is known as mental proliferation (papanca).

If you are practicing Vipassana meditation, then simply note these mental formations as "thinking, thinking" and return attention the rising and falling of the abdomen.

If you are practicing Samatha Meditation, then simply acknowledge the thoughts and return to your primary object (nostrils, upper lip or abdomen).

Do not dwell in in those thoughts. Do not attach to them. They are merely impersonal phenomena, arising and ceasing on their own accord, due to causes and conditions.

Continuous thinking leads to latent tendencies.

“Bhikshu, as regards the source from which proliferation of conception and perception assails a person: if one were to find nothing there to delight in, nothing there to welcome, nothing to cling to—this is the end of

• the latent tendency of lust,
• the latent tendency of aversion,
• the latent tendency of views,
• the latent tendency of doubt,
• the latent tendency of conceit,
• the latent tendency of desire for existence, and
• the latent tendency of ignorance.

This is the ending of the taking up of the rod and the sword, quarrels, disputes, mayhem [strife], slandering and lying —here these evil unwholesome states cease without remainder.”

…

Avuso, dependent on the [eye | ear | nose | tongue | body | mind] and [form | sound | smell | taste | touch | mind-object], [eye | ear | nose | tongue | body | mind]-consciousness arises.

• The meeting of the three is contact.

• With contact as condition, there is feeling.

• What one feels, one perceives.

• What one perceives, one thinks about.

• What one thinks about, one mentally proliferates.

From that as source, proliferation of conception and perception assails a person regarding past, future and present [forms | sounds | smells | tastes | touch | mind-objects] cognizable through the [eye | ear | nose | tongue | body | mind].

Madhu,piṇḍika Sutta

Best option is to drop it and get back to meditation. Also thinking gives and intellectual stimulation.

vi. On cognizing a mind-object with the mind,

• one investigates the mind-object that the basis of mental joy,
• one investigates the mind-object that is the basis of mental pain,
• one investigates the mind-object that is the basis of equanimity.

Dhātu Vibhaṅga Sutta

Regardless of that they are stimulating and pleasant or depressing you should not get averse or attached to them.

(1) the latent tendency to lust reinforced by being attached to pleasant feelings;

(2) the latent tendency to aversion reinforced by rejecting painful feelings;

(3) the latent tendency to ignorance reinforced by ignoring neutral feelings.

Pahāna Sutta

When you get distracting thoughts, look at what sensations they have produced, i.e., they were pleasant thoughts or unpleasant thoughts. Stay with the sensation equanimously for a while until it subsides and then return to your object of mediation.

I don't know if this helps to answer, but I take it as axiomatic that there are bad actions, bad intentions, bad habits, bad environments ... but not "bad people".

If a child bites one of their class-mates, for example, the teacher shouldn't say "you're a bad boy": they should say "don't bite people", or, "use your words instead of biting", or something like that.

I think that Buddhism might tend to discourage adults from thinking you're "a person" at all of any kind, good or bad. And I think that a question to ask is not, "Am I a bad person?", it is, "Is this good behaviour? Good intent?", and so on.

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

If you return to your breathing, your mind can feel calm. If your mind feels calm, it will not have the habitual (compulsive) thought.

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?

No. If your mind can feel calm by focusing on your breathing, your subconscious will start to believe: "I can be a calm person" instead of "I am a bad person".

It's holding me back from meditating because I feel uneasy about dropping the thought.

You & nobody else can benefit from meditation if it is believed: "I am a bad person". Therefore, I recommend two options:

(1) Ignore the thought & focus on your breathing, until you start to believe: "I can be a calm person".

Otherwise:

(2) Address the thought & change it to: "I am not a bad person. I am just an ordinary person. I am a person who wants to improve my life & be a better person."

The Buddhist path has more components than only focusing on breathing. The other components include to stop doing harmful (negative) actions & to develop love & compassion towards yourself.

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.