I can't know the specific reasons or motivations of your ex-girlfriend, as I don't have access to her thoughts or emotions. However, I can offer some general insights that might help you understand her behavior.
Hurt feelings: It's possible that your ex is still hurt or upset about the way the relationship ended or the mistake you made. Even though she started dating someone else, she may not have fully processed her emotions from the past relationship.
Guarding emotions: Sometimes, after a breakup, people build emotional walls to protect themselves from getting hurt again. Being cold and distant with you could be her way of guarding her heart and avoiding getting entangled in past emotions.
Moving on: While she may have started dating someone else, it doesn't necessarily mean she's over the breakup or has entirely moved on emotionally. Jumping into a new relationship could be a way to distract herself from the pain or to prove to herself that she's fine without you.
Self-preservation: If you hurt her in the past, she might be cautious about allowing you back into her life to protect herself from potential pain or disappointment.
Maintaining boundaries: Keeping a distance and being unfriendly might be her way of establishing boundaries and signaling that she's not interested in rekindling the relationship.
It's essential to respect her feelings and space. If you genuinely regret your past actions and want to reconcile, give her the time and space she needs to heal and process her emotions. Show her through your actions that you've changed and are genuinely sorry for any hurt you caused. However, it's important to recognize that reconciliation may not be possible, and you should be prepared for that outcome as well. Focus on personal growth and learning from the mistakes to improve future relationships, regardless of the outcome with your ex.