More like "whenever one of an inherently-coupled pair of actions is morally allowed, the other of those actions is morally allowed". A moral system which allows one and not the other is self-contradictory.
In this case, a moral system which permits the right to sell a life but denies the right to buy a life self-contradicts; unless you believe that it's moral to trick someone into committing an immoral act (I do not), any attempt to exercise the right to sell one's own life would be inherently immoral because of the impossibility of doing so without causing someone else to perform an immoral act. The only way for the sale of one's own life to be moral is for the corresponding purchase to also be moral.
"we end up with a moral dilemma"
Only if you insist that buying is wrong while also insisting that selling is not wrong. When both are right or both are wrong, then there is no such self-contradiction.
Why does that follow? I could understand it for actions you are morally obliged to do, but I fail to see why it follows for actions which are merely allowed.
A 6-year old boy is allowed to fall in love with his teacher, but she is not allowed to fall in love with him, so his love - even though morally allowed - can never be fulfilled. That is a perfectly fine situation, from a moral point of view.
This does not stand on its own, you need to provide a good argument why a moral system should be designed such that everything which is allowed can also actually be done. In particular, because our current system is not designed that way.
And even if you find such an argument, we end up with a moral dilemma, as long as you can't argue that buying is morally good in itself.