So where does this relationship anxiety come from?
One of the major theories regarding relationships is called attachment theory. It suggests that the way you related to your caregiver as an infant (and vice versa) shapes how you come to view relationships later in life.
If your caregiver was attuned to your needs and responsive, you will develop a secure attachment. That means you are comfortable with close relationships because your experience paid off -- mom or dad was there when you were distressed or hungry or cold. From that experience, you learned that relationships are safe and reciprocal, and your attachment anxiety is low.
But if your caregiver was not so attuned to your needs, was intrusive or inattentive, you might develop what is called an insecure attachment. If something you wanted emotionally or physically (like comfort) went unfulfilled, you might end up anxious about relationships as an adult. You might realize that relationships may not be trustworthy, not invest in close relationships, and avoid intimacy all together.