There could be several reasons why your ex continues to watch your Instagram and Snapchat stories even months after the breakup. While I don't have access to specific information about your situation, here are some possible explanations:
Curiosity: Your ex might be curious about how you are doing post-breakup. They may want to see if you've moved on, how you're spending your time, or if there are any significant changes in your life.
Nostalgia: Watching your stories might evoke feelings of nostalgia and remind them of the time you were together. Even if they initiated the breakup, they could still have sentimental attachments to the past.
Habit: During your relationship, it's likely that you and your ex were frequently connected on social media. Checking your stories could have become a habit, and they might not have consciously stopped doing so after the breakup.
Regret or Second Thoughts: Sometimes, a person who initiated the breakup may have second thoughts or feelings of regret afterward. Watching your stories could be a way for them to maintain a connection or gauge whether getting back together might be a possibility.
Monitoring: Your ex might be keeping an eye on your social media to monitor your life, potentially out of concern or jealousy. This behavior may be an attempt to maintain a sense of control or stay informed about your current situation.
Loneliness: If your ex is feeling lonely or struggling emotionally after the breakup, watching your stories might provide them with some comfort or a sense of familiarity.
No Negative Intentions: Sometimes, the act of watching stories may not have any significant underlying meaning. They might simply be browsing through their feed, and your stories happen to appear.
It's important to remember that the reasons for their behavior can be varied and complex. If you feel uncomfortable with your ex continuing to watch your stories, you have the option to adjust your privacy settings or consider blocking or removing them from your social media contacts. Taking steps to create distance can be beneficial for your emotional well-being and help both of you move on from the past relationship.