Early on, the book makes it pretty clear that it's a control issue, not a physical impossibility. Edward is so much stronger than Bella, and his instinct to consume her—her blood, specifically—is constantly at war with his desire for her. A kiss isn't just a kiss for them; it's a moment of extreme vulnerability for him where his primal hunger could take over. He's terrified he'll lose his grip, even for a second, and hurt her. It's less about his marble lips and more about the monster inside him that sees her as the ultimate temptation.
This gets highlighted in the infamous 'almost kiss' scene in 'New Moon' after the birthday party disaster. The separation happens because he grazes her throat with his lips while trying to stop the bleeding, and the scent of her blood is overwhelming. That incident retroactively justifies all his earlier hesitation. The restraint is a daily, moment-to-moment act of love for him, which, I gotta admit, is the core of the series' romantic tension for a lot of readers. It frames his love as this incredibly disciplined, protective force, which is the whole fantasy.
Thinking about it now, it's a clever metaphor for teenage sexual anxiety, drawn in supernatural terms. The fear of going too far, of losing control and causing irreversible damage, is literalized through his vampirism. The explanation isn't in a single line of dialogue; it's woven into every interaction where he flinches back or holds himself perfectly still.