To put it as plainly as possible, a truly healthy relationship is a secure one. At the end of the day, people in secure relationships feel comfortable allowing their partner to have a bit of independence while also being able to reach out to their partner when they need love or support. In a secure relationship, there is an abundance of trust and understanding. This, according to PsychCentral, is the end goal. Though altering an attachment style can be difficult since it is formed from a young age, there are ways to recognize the behavior and alter it before it affects your relationship in a negative way.
Especially for those who identify with the anxious-preoccupied attachment style, being in a relationship with someone who has a secure attachment style can also help them feel more secure. Classic anxious-preoccupied folks will also benefit from working on raising their self-esteem on their own time, since much of their troubles stem from a low self-worth.
If you relate more to Barney's desire for emotional independence (and absolutely detest being dependent on someone else to fulfill your emotional needs), psychologists suggest taking more risks. Instead of playing games and attempting to manipulate every romantic interaction, try instead to be authentic and direct. And lastly, those with a mix of these two attachment styles can simply benefit from remaining true to their own emotional needs by voicing them and talking about them with a romantic partner (per PsychCentral).