The people I've truly cared for and who have cared for me I rarely if ever feel anxious around. Anxiety has to do with having false-values, and wanting something for your own self-image that you either are worried about losing or not having and feeling that you need. Insecurity comes from not realizing that the only person that can define and give shape to your life is yourself. Only your actions of how you treat others are in your control and those alone define who you are as a person. Most people yearn for validation from others and though they may receive it it's only a temporary fix while understanding that we are who we choose to be reminds us that we are our treatment of others rather than how others treat us.
Anxiety is fear of the unreal. Both of what may or may not be true but also the unreal in terms of grounding yourself in that which is outside of your control and the Ego which is vicious and always seeking its own temporary satisfaction rather than engaging in meaningful and virtuous conduct. Virtue is that which is self-sufficient, and therefore what we have anxieties over is not virtuous. We may believe it's for a virtuous cause or pursuit, and though there may externally be ethical conduct there (feeling anxious about your job organizing a political campaign to fund special needs programs for example) internally our frame of mind is focused not on the goal but what achieving the goal (or failure to do so) says about us. We are then driven for the image of success rather than actually succeeding in that which is the good and this focus on self-image is derived from insecurity which is the source of anxiety.
We must always remember the good in us and keep true to it rather than seek for external validation which is never centered on virtue but instead of things like fame, reputation and money. Virtue is that which psychologically is focused on "the-thing-in-itself" then and not the illusions which pervade much of our world. This is why only through virtue can we be reliably happy and act in a way that has us concerned with good action, rather than the social perception of good action.