Edward is a loner and shitty movie marketing
The biggest character mistake in the Hollywood marketing for the Twilight movies was attempting to brand Edward Cullen as an insanely charismatic 'ladies' man', 'too sexy for his own good', when this is a blatant misalignment with his behaviour/personality.
He's reclusive and an emotional train wreck, with no experience with romantic relationships/intimacy, buried in shame (catholic guilt variety), and BRUTALLY negative self-perception.
He's strange, even in a room of vamps due to his telepathy (as I've mentioned before, his social aid and disabler) and of course, his guilt, shame, and repulsion of being a 'monster'.
His positive traits include his dedication to music, literature, and acquisition of knowledge (for instance, medicine, *for Carlisle), he's extremely physically capable (vamp perk), so by extension, you could say he's athletic, but that doesn't negate his inherent nerdiness.
Edward is the quiet kid who represses all his emotions (until they burst, or rot inside). A perfectionist who maintains extreme 'order' outside to compensate for the inner chaos. He's the kid who is not 'disliked' because he's a 'genius', a musical prodigy, a chess master (also pretty privilege)…Ultimately, his intensity is intimidating, and his lack of interest in social hierarchy alienates him.
Some of it is the rose-tinted glasses Bella perceives him through (less we forget Bella is also socially alienated and a self-declared 'freak'). But who can blame her? From the outside, he is brilliant, intelligent, charming even (when he controls his 'monster' self), and ofc 'exceptionally beautiful'. However, Edwards' suffering is internalised; he spent 100 years refusing to be vulnerable, he built unshakeable walls around his heart/soul, and then throughout the storyline, the relationship with Bella is what begins the demolition process (which is messy, confusing, chaotic). His coping methods are turned on their head; subsequently, he has more nervous breakdowns, paranoia, a desperate need for order, control, and predictability (extra neurotic).
All this to say, I completely understand why critics will look at the hype/adoration/glorification of his character, which has become almost archetypal (Mysterious and Sexy Danger Man), and then assess the behavioural traits he exhibits (the movies are particularly bad at complexity/nuance), and be taken aback by the contradictions..."Are people this delusional" and the answer is yes, and no, for one it is the marketing which pushes this narrative and most people lack the critical thought or incentive to question it...because he's hot... and sexy... and dangerous...So I can't blame individuals for having a warped conception...
Perhaps, I'll explore how the 'love triangle' is grotesquely exaggerated for marketing, again, of course.