First of all good question. I tried myself on that one, but if any other member of this wonderful site has additional input please also answer :)
In a monopol we know there exists a consumer who would be willing to pay a price for an additional unit of the good that is higher than the additional cost to produce that unit. Possibility of Pareto improvement: monopolist produces one additional unit and receives marginal cost from consumers. Giving away one unit for marginal costs does not make the monopolist worse off in the first case. But if the monopolist wants to sell an additional unit, he must lower the price not only for the last unit, but also for all remaining units. This is the result of one critical assumption: no perfect price discrimination. But from the perspective of a social planner one could produce an additional unit and find a trade where $MC \leq P$ by allowing the monopolist only to change price for its last produced unit. In absence of such a planner the monopolist falls back to the old logic.
This leads us to the definition of market failure: individual rational behaviour leads to collective irrational outcomes.
Pareto optimality is also a very narrow definition, take for example the Kaldor Hicks criteria which states: An economic policy measure is welfare increasing, if in the society as a whole, increases in benefits outweighs the losses of benefits. This simply means winners could compensate losers, or in other words the sum of gains needs to be greater than the sum of losses (independent from individual changes). This holds true for the destruction of the monpoly because sum of consumer and producer surplus will increase. The pareto criterium is often criticised to favourite the status quo, while Kaldor Hicks creates more possibilities for restructuring in exchange for violating the methodological individualism.