An important reason that it is unfair to force a being to stay alive is that the being took no voluntary action in order to come into being.
Voluntariness is a key element of fairness is much of our legal system. Our law of contract requires that the parties voluntarily enter the contract in order for it to be enforceable. Likewise, marriage must be entered voluntarily, or it is not legally effective. Crimes require a voluntary act before punishment may attach. (See note.)
Given this framework, voluntary procreation (choosing to have children) has two important consequences. One, given that the act of procreation forces existence on others, it may be a moral harm in and of itself. Second, and more relevant to our purposes, procreation is a voluntary act, like signing a contract, that creates a moral obligation for the parent toward the child. A non-parent (or an involuntary parent, such as a rape victim) has given no assent to life, and retains the right to remove himself from the world; the voluntary parent has given his assent to life, and created obligations toward his child.
An interesting question is whether there are acts other than voluntary procreation that cement the agent to the world, potentially destroying his moral right to suicide. One candidate would be intentionally forming or continuing a close relationship; although of course this does not involve creating an entire new being dependent upon the agent, it does, perhaps, encourage others to become dependent upon the agent. Perhaps potential suicides have a moral obligation not to form or continue close relationships, just as they have a moral obligation to avoid procreation.
(Note that voluntariness cannot account for the basis of authority of the state over people who have not consented to be governed by that state. In a state with a broad suicide proscription, in which there is even less of a possibility to "opt-out" of state control, the authority of the state over non-consenting individuals is weaker than in a state where life is not compulsory.)