This is, after all, a defining feature of anxiety disorders.
Note that he doesn't say that this kind of fear in itself is not rational (propensity towards it might come in handy in certain social situations), but the degree of this kind of fear in the contexts that a diagnosis demands is totally irrational.
Even if we set aside the fact that the disorder in question does not deal with rational things, one can easily argue that (in this context) the text is more permanent, and can potentially reach many more than unrecorded spoken language.
Downsides include the opportunity to get stuck in a loop of doubt and rewriting the entire post. Misinterpretation of the written word is also common. Therefore, the trademark anxious rumination is not less likely to occur by virtue of the medium alone.
Some sufferers of social anxiety might be anxious in these settings, others might not.
All in all: interpretation based on assumptions helps no-one.
i can't say i have social anxiety, but i feel very similar in this instance. and, if i can judge based on this statement alone- i don't think it's fair for you to say your fear comes from "no rational reason".
a very rational reason to be afraid of verbal communication as opposed to text, is that text is a much easier medium to control your message.
there are a dozen benefits: you have more time to parse and consider what one says to you, you have more time to formulate your thoughts clearly, you are less open to your words or tone being misinterpreted, etc.
are you anxious right now? this is very much a social setting. if not- and i hope this doesn't sound insensitive- i'm left wondering, whats the difference? and, would identifying the difference help you overcome your anxiety?