Lets use the example of an unwillingness to apologize to illustrate the Twelve Nidanas of dependent origination:

1. Ignorance (avijja): The person lacks understanding of the true nature of reality, including the importance of taking responsibility for ones actions and behaviors.
2. Mental formations (sankhara): Due to ignorance, the person has formed habitual patterns of avoiding taking responsibility and making apologies.
3. Consciousness (viññana): The persons consciousness is conditioned by these mental formations, making them prone to being unwilling to apologize.
4. Name and form (nama-rupa): The persons body and mind manifest in a way that is resistant to apologizing and taking responsibility.
5. The six sense bases (salayatana): The persons sense organs interact with the external world, including interactions with other people and situations that may require an apology.
6. Contact (phassa): The person encounters a situation in which an apology is warranted, either through their own actions or through the actions of others that affect them.
7. Feeling (vedana): The person experiences an unpleasant feeling when considering making an apology, such as shame or guilt.
8. Craving (tanha): The person develops a desire to avoid the unpleasant feeling associated with apologizing, and they may seek to protect their ego or self-image.
9. Clinging (upadana): The person becomes attached to their desire to avoid apologizing, leading to further resistance to taking responsibility for their actions.
10. Becoming (bhava): This clinging reinforces the persons habitual patterns and karmic tendencies, perpetuating the cycle of avoidance of apologies.
11. Birth (jati): The persons unwillingness to apologize manifests in their actions and behaviors, leading to negative consequences such as damaged relationships.
12. Old age and death (jara-marana): Unaddressed unwillingness to apologize can lead to ongoing conflicts and suffering, perpetuating negative consequences in future situations or even future lives.

In this example, we can see how the Twelve Nidanas apply to the perpetuation of an unwillingness to apologize. By understanding the cycle of dependent origination and recognizing the interdependence of the Twelve Links, a person can gain insight into their own negative patterns around apologies and work towards breaking free from them, ultimately leading to greater peace and positive relationships.

How to break cycle at each point:

In the case of an unwillingness to apologize, one can break the cycle of dependent origination at multiple points:

1. Ignorance (avijja) - By recognizing the importance of taking responsibility for ones actions and behaviors and acknowledging the impact it has on oneself and others, one can break the cycle at ignorance.

2. Mental Formations (sankhara) - By cultivating a habit of taking responsibility for ones words and actions, one can break the cycle of deflecting blame onto others and avoiding apologies, thus breaking the cycle at mental formations.

3. Consciousness (viññana) - By developing awareness of ones thoughts and actions in relation to apology and taking responsibility, one can prevent distorted perceptions and self-importance from influencing their actions and break the cycle at consciousness.

4. Name and Form (nama-rupa) - By cultivating flexibility and openness in ones thinking and behavior, one can avoid being stuck in a pattern of defensiveness and stubbornness, thus breaking the cycle at name and form.

5. The Six Sense Bases (salayatana) - By developing awareness of how one perceives and interprets external stimuli, including the opinions of others, one can prevent defensiveness and misunderstandings that might interfere with making a sincere apology, thus breaking the cycle at the six sense bases.

6. Contact (phassa) - By remaining open to the impact of criticism and feedback from others, one can avoid reacting defensively and instead use it as an opportunity for self-reflection and growth, thereby breaking the cycle at contact.

7. Feeling (vedana) - By recognizing and acknowledging feelings of shame, guilt, or anxiety that may arise in relation to taking responsibility and making amends, one can prevent the resistance to these emotions from interfering with the cycle of growth and healing, breaking the cycle at feeling.

8. Craving (tanha) - By recognizing the importance of taking responsibility for ones words and actions and acknowledging the impact it has on others, one can prevent the desire to avoid discomfort from hindering the opportunity for reconciliation, thus breaking the cycle at craving.

9. Clinging (upadana) - By avoiding reinforcing negative patterns of thought and behavior, one can prevent oneself from getting stuck in unproductive feelings of guilt, shame or anger, instead moving forward with owning ones actions and making amends, thus breaking the cycle at clinging.

10. Becoming (bhava) - By embodying intentions of accountability and growth in ones speech and behavior, one can break the cycle of negative patterns in relationships and ones life, breaking the cycle at becoming.

11. Birth (jati) - By taking responsibility for ones actions and behaviors, one can prevent further damaging relationships and accessing negative karmic tendencies, preventing birth from turning into further negative consequences, thus breaking the cycle at birth.

12. Old Age and Death (jara-marana) - By making sincere apologies and taking responsibility for ones actions, one can prevent ongoing suffering that may result from unaddressed issues of accountability, thus breaking the cycle at old age and death.

In summary, breaking the cycle of dependent origination at each point requires awareness and mindfulness of ones thoughts, feelings, and behavior in relation to taking responsibility and making amends. By cultivating these qualities, we can work towards breaking the cycle of ignorance, defensiveness, and negativity in our relationships and our lives, fostering growth and greater positive growth and insight.