Being self-confident and self-critical are not mutually exclusive.
Being self-critical and self-loathing are not the same thing.
I can love myself and think highly of myself, and still recognize my shortcomings. And I can be disappointed in myself for not meeting my own expectations without demeaning myself or my self-worth.
There are times when I feel like I can come off as arrogant or narcissistic, especially in social situations. But that persona has really just developed as a defense mechanism, a fake-it-till-you-make-it type of thing. It’s a narrative I tell others, and myself, to affirm that I am worth my time here on Earth. I used to deal with a lot of “self-hate”; feelings of inadequacy, of unworthiness, imposter syndrome, etc. Much of that I still struggle with to this day, but I think I’ve learned to cope with it better over time. Like many people, I deal with some of this through humor, but for me being self-deprecating is often too real and actually depressing. So instead I’ll lean into small/ insignificant virtues or compliments because in my head the suggestion that I excel at something (usually trivial or pointless things) is funnier than fixating on my flaws, which are obvious to me and, in my mind, are obvious to everyone around me. But now it’s gotten to the point were some of that bleeds out into serious conversations, and it can sound like I seriously think I’m better than everyone around me.
To some extent I did always think I was “special,” I just wasn’t convinced that I was special in ways that mattered to anyone else, especially given what society and the media tells us makes a person valuable. Those feeling are compounded by rejection; putting your genuine self out there, hoping that someone, somewhere, will find value in the things you value about yourself, only to be ~gently~ informed that you are not quite “special” enough. Even if you are validated at some point, the specter of all the past, and future, rejections perpetually lingers in the background waiting for any opportunity to pop out and say “I told you so” (as you can tell the medical application process has done wonders for my self-esteem).
Through all this it’s easy to get mad at the world and in your own way try to reject the world for rejecting you. The only problem is (1) “the world” probably won’t even notice and (2) “the world” doesn’t deserve that kind of effort from you. Your value is not dependent on others’ ability to see it or not, and your time is better spend on yourself.