You are taxed on this in the UK: https://www.gov.uk/guidance/check-if-you-need-to-pay-tax-whe... - it's an instance of these rules, which apply to most types of asset: https://www.gov.uk/hmrc-internal-manuals/capital-gains-manua...
You're not taxed, because the tax authorities rely on self-reporting. Trading one asset for another asset is ~always a taxable in most (all?) countries.
Well not in France at least, and as far as I know this is the same in most EU countries. I do not really know for Asia and Africa though, but I only ever heard of US (and now of UK).
I will add that in some EU countries you are not taxed at all (assuming this is not your day job), even when converting to fiat ! Portugal, Belgium and Germany. Also Switzerland (not in EU)
So using stablecoins is a way of securing volatile crytpo assets for any period of time, while not having to pay taxes immediately (only when you decide to convert to fiat)
Of course this makes sense only if the stablecoin is actually stable ...