How can my ex move on like we never mattered?

Breakups from long term relationships are very tough and what you have witnessed is even tougher.  Breakups can paralyze us and leave us trying to put the pieces back together again.  Breakups do give the opportunity to self reflect and grow, but it is hard to see any positives when we are feeling the emotional pain from the breakup.  There is a normal process of healing, much like the grief process from any event of loss.  We will often be in denial at the beginning and then spend some time in anger, depression, or even bargaining until the point we come to true acceptance.  It is normal to look at what went wrong and critique ourselves in the relationship.  We also sometimes have regrets.  We have to be careful not to get into a euphoric recall of the past relationship, which we tend to minimize all that wrong in the relationship and just focus on the good times.  It is important even to write down the things we did not like about the relationship and remind ourselves in a more balanced way the reasons the relationship did not work.  For certain attachment styles based on our childhood attachment, breakups can be easier or much harder.  An avoidant attachment style (the type of person who has a hard time emotionally connecting to others), breakups are generally easier and the person is largely just able to move on quickly.  For anxious attachment styles, a breakup is very devastating and usually consumes the person almost completely which can lead to numerous mental health issues.  People with secure attachment are more in between, a breakup may hurt but they are able to process and move on in a healthy way. 

I would say that many times things after a relationship are not what they appear to be on the surface.  For example, if your ex has an anxious attachment which seems likely by her begging to stay with you, she has almost a love hole that cannot be filled.  With this attachment style, she would probably be devastated by a breakup because she would have a great fear of being rejected and being alone.  I am not saying this is her and what occurred, but it is definitely a possibility.  Insecure attachments like anxious attachment come from past experience likely related to how a person attaches in childhood.  If she does attach this way, she would have presented in the relationship as very needy, needing constant reassurance and validation , and likely needing high amounts of affection.  This type of attachment attaches very hard and falls very quick.  They love "hard" but also are difficult to maintain relationships with due to their almost constant need for attention and reassurance.   With this attachment style, the flip side is that they do terribly in breakups.  The deep insecurities and the intense feelings that are generated by feeling rejected are almost too much to take.  The problems with this is often complicated by the "trigger" of the breakup resulting in a very acute emotional reaction.  This would explain why she begged for you to come back.  As such, it is common for people with this attachment style to seek almost immediate replacement affection and validation to stop the emotional pain from the breakup.  The reason I suspect this is that the person immediately got involved with someone else and seemed to be immediately "in love" on social media.  However, this is all just a smoke screen for what is really going on even if she is not aware.  This is a bandaid attempt to avoid the pain and feelings from the breakup.  She is likely not really all into this person as much as quickly attaching to this person.  I know this may not help, but what she has done does not make the emotional connection you had with her any less.  It may just be a reaction to the breakup.   She cannot stand the feeling of being rejected and being alone which results in a poor boundary attempt to start something new and bury the real issue. 

You, on the other hand, with whatever attachment style you have, are choosing to face your pain and fears and starting a process of healing in your life.  It is fine to be angry, it is fine to feel hurt, it is fine to cry tears.  This is hard on you and the worst thing you could do is bottle up your emotions or try to put a bandaid cure on them.  I encourage you to really focus on self care and self love.  Take care of yourself, do self loving things.  Write 10 positive self affirmations and put them on your mirror.  Read them before you start your day.  Find some way each day to give yourself some sort of treat.   Reach out to the people that love you and find support.  Do not isolate even if that is what you want to do.  Take care of your body, exercise and try to eat healthy.  Try to get into good sleep patterns.  Journal about how you feel and give yourself the ability to better process your emotions.  I would also encourage you to stay in therapy for a while.  Heal from this relationship and learn about you and how you can be the best you.  Be patient with yourself and realize that healing will take time.  As discussed earlier, realize there may be more to this than there seems and do not diminish the relationship you had.   Try, as much as possible, that this may be a reaction and is likely not a direct rejection toward you.  Love yourself and accept yourself through this process.  Manage your anxiety better through learning and practicing grounding techniques.   And don't stop believing in yourself.  You can get through this and there will be brighter days ahead.