He says: "Either you have a right to X or I have a right to stop you from getting X. You can only choose one.
Therefore, everybody supports an equal amount of rights, they only differ on which rights we should have.
Libertarians dishonestly think they support more freedom than other people."
Many ideologies, and libertarianism is one of the worst offenders, claim that they want to maximize individual rights and freedom. The problem is, every right the government (or nature, if you want to dabble in mysticism) confers on us is balanced by a right taken away from others. My right to religious freedom infringes on your right not to be proselytized, or your right not to hear the prophet denigrated. My right not to get punched in the face no matter how much I deserve it is offset by depriving you of your right to punch me in the face. And so on. All ideologies differ only in that they value some arbitrary set of rights over another equally arbitrary set of rights.
Libertarians often try and circumvent this dilemma by claiming to only support those rights that don't involve coercion or the use of force. In this, they're sadly deluded, because theft requires neither, while the punishment of theft employs both. There's nothing coercive or violent about swiping everything that's not nailed down, while summoning the police to imprison or shoot me if I don't respect your invisible claims to property is the epitome of coercion.