Your future lies ahead of you and not behind you.
That's my philosophy in life. I have never been "haunted" by memories of an ex. I've never had a "mere" breakup. I believe those that do are generally immature. They don't do any (introspective thinking) prior to making a final decision to end their relationships.
More often than not they breakup "spontaneously" during a moment of anger or disappointment. This leads many of them to have "yo-yo" relationships where they breakup and makeup frequently. When you think something through first it's permanent.
Another reason why people want to (go back) is because it's "comfortable" and they have "romanticized" the past. They only remember the "good" times. Breakups occur over "differences".
When you're in love with someone I believe you should give it your best. Having said that if my ex wanted to get back with me I would kindly reject them. There's nothing more I could give than my (best) and that was not good enough to make the relationship work the first time! Unless two people have changed their (core being) and are radically different from what they were they're likely to have the same results if they got back together.
Last but not least one should keep in mind some people just want to "prove to themselves" they can get back with anyone they have been with in their past. It's an ego exercise for them. It's also possible when they "moved on" they got dumped! This makes them want to go back to someone who will accept them until they're ready to move on again. Ultimately it's not just about what (she/he wants). Life is a personal journey and you are responsible for your own happiness.
“Being with no one is better than being with the wrong one.” - Anonymous
“Giving up doesn’t mean you are weak! It only means that, you are strong enough to let go.” – Unknown