Under a frequentist interpretation of probability that's correct (and the paradox doesn't arise), but Bayesian decision theory does allow you to reason in the way the paradox proposes, starting in a situation where you've already picked an envelope, and estimating the utility of switching to the other one by multiplying the probability that you're in the high->low configuration with the value of a high->low switch, and likewise with a low->high switch. So you have 50% chance of halving your money, 50% of doubling, and thus estimated 1.25x return.

Frequentist probability doesn't let you do that, because it doesn't let you say "there's a 50% likelihood I'm in this state, and 50% that I'm in the other". Instead, it says you must be in one or the other state (non-probabilistically), and the probabilities are only attached to a previous process that generated that outcome. But Bayesian probability does let you interpret the probabilities as belief in each current state, so you have a 50% belief you're in one state, and a 50% belief you're in the other, and the value of any decision is thus 0.5 * value_if_I_was_in_situation_A + 0.5 * value_if_I_was_in_situation_B.

(If you don't allow that kind of computation, Bayesian decision theory has to be revised in some other cases as well.)