When you use the word "this" in a sentence, do you have to specify to what you're referring? Someone told me it's better to. Is this rule true or is it just to do with style?

(If that doesn't make sense, here's an example:
"Harry was bitten by a dog when he was three."
Would it be better to say "Because of this he now avoids dogs", or "Because of this experience he now avoids dogs"?)

It's a good question. You can use both. If your standalone "this" is too far from the words it replaces, then it may be preferential to help the reader by making adding another word to make it absolutely clear.

I see this question more often with "both". i.e. is it okay to use "both" without referring to what you're talking about again? The answer is yes.

People are clever. They can remember topics from one sentence to the next.

The rule is:

If it's clear what it's replacing and you're content with how it reads, then use "this" by itself.