So much of the time people respond to a breakup with desperation, panic, and fear. Those three mental and emotional states almost never allow you to react in productive ways. When someone has told us that they want us out of their life, the best way for us to respond is to give them what they want. You will appear like a psycho stalker if you continue to pursue and pester them. It will be like you saying that even though they want a certain thing for their life, you don't and you are putting your wants and needs above theirs. That only makes you look selfish and out of touch. It will certainly push your ex away even further and destroy your chances of getting them back. As a dating coach with my specialty being in breakup recovery, I can tell you that the best way to handle a breakup is by being calm and graciously bowing out of the person's life. That way you look good and your ex has an opportunity to miss you. If you pester them, text, call, and otherwise nag them to come back to you, your ex cannot miss you but actually wants you gone even more because you are annoying them and making things very awkward. It's very important that, in spite of the difficult emotions, that you keep calm and show your ex that you respect his/her wishes. You must give them the breakup if you want a chance at getting them back.
Infographic Source: https://myexbackcoach.com/just-dumped-do-this/
