I haven't read that poem so won't talk about it .
We might remember a girl who got away for myriad of reasons of which I will list a few.
We might remember her becuase of her qualities-her physical attributes,her nature,her intelligence .
We might remember her for the effect she had on us-made us feel good about ourselves,inspired us to do better,be a better person and stuff like that.
A person might be just some narcissistic, egotistical maniac who could not bear that he did not get a girl he desired and will always remember her.
He might think his present life with his wife/gf is not great and things might have been better if he had been with her.
Finally grass seems to be greener not only on the other side but also on grasslands we have left behind even if we are grazing on some fantastic grassland. Human nature !!!!