One way around social anxiety: think about how little you care about the person in front of you. If you heard that they died how long would you be thinking about it? That’s how much they care about what you do. Or don’t do.
You're assuming that anxiety can be mitigated by just logically convincing oneself that there's no need to be anxious. This might be the case for some people, but for many of us it's a fundamentally irrational condition; the issue isn't that I think something bad will happen if I talk to someone and make a mistake, it's that sometimes having to talk to someone _is_ the bad thing I don't want to happen. You've probably met people who are afraid of spiders, or snakes, or something of that nature, even the ones that don't pose a threat, and the issue is similar here;
But anxiety CAN be mitigated by logically convincing yourself that there's no need to be (as) anxious in the moment. That's the whole point of various forms of behavioural therapy: to teach you ways to arrest spiralling, maladaptive thoughts and lead them to a more functional landing.