I think it's a pretty lopsided debate from the get go.
People will subconsciously sway towards agreeing with "positive" rights because positive = good. And people will naturally avoid "negative" rights cuz neg be bad.
And in fact, I think whoever designed these terms for political science knew that he or she was giving themselves, and their ideology, an advantage from the start.
Control the language of an argument, and you control the argument.
Except the theoretical underpinning for the distinction is pretty obviously due to the nature of the concept itself. The "negative" merely references that the right in question limits or forbids rather than requires government action. These terms are rarely used in popular discussions in any event, usually occurring in philosophy of politics or legal academic discussion, and the distinction, I believe, has largely become important in conservative legal academia. You will encounter a lot of opposition to positive rights, using that term, in organizations like the Federalist Society.
I think the distinction is largely meaningless, in any event. Take the most central negative right, the right not to be killed. Unless you're going to separate that out into a right specifically not to be killed by the government itself and a somehow different right not to be murdered by other people, it presupposes some sort of enforcement, whether before or after the fact.
Prior to modern civilization, while this right was recognized, it took the form of the right to take revenge against those who killed someone in your clan or tribe, with little formal distinction as to what circumstances justified this. Naturally, groups disagreed on what triggered or satisfied this right, and with two sides claiming justified reprisal against each other, endless feuds were more the norm than the exception.
Eventually, monarchs and other rulers of larger societies comprised of these smaller groups realized the inefficiency of this, and supplanted it with systems allowing for fines or other forms of compensation for unlawful killings, and established codified forms of adjudicating when these were justified and when they satisfied the debt incurred thereby. These evolved, eventually, into courts with actual written laws, judges, juries, and other formalities intended to ensure fair or at least consistent application of these principles.
The covenant established essentially traded a previously recognized right, the right to revenge, with a right to access to a system that promised compensation for wrongs done in return for foregoing justified vengeance. This sort of vengeance would, subsequently, be viewed as itself a crime in the same sense as the original act.
How does this relate to negative and positive rights?
It's fairly simple. The supposedly negative right simply not to be killed, the most obvious of negative rights, in actuality requires a rather vast infrastructure of law enforcement and a judicial system, in order to have any meaning at all. Without any means of discouraging or preventing unlawful killings, things would rapidly revert to the pre-legal means of handling it, with predictable results.
Even an obvious "right not to have this done to you" requires a functional society to enforce it.
This should be distinguished, incidentally, from positive and negative liberties, which are to some extent their philosophical converse.
Much as with the rights, though, the U.S. system in particular generally tends to frame these as negatives rather than positives.
For instance, in relation to the right not to be killed, there is a positive liberty that one is entitled to self-defense. While that particular right is so fundamental to any ordered society that it is not specifically enumerated in the Constitution, the U.S. recognizes the specific right to defend oneself with arms. However, rather than specifically elaborate on the right itself, the Second Amendment prohibits the federal government (and now the states via the Fourteenth Amendment) from infringing the right. Similarly, rather than explicitly commanding a freedom of speech, the First Amendment instead prohibits Congress, the branch of government with legislative authority, from passing laws infringing it.
So when one discusses even the simplest seeming right, like the right not to be killed, that isn't one atomic thing that can not be subdivided or dissected. It's a bundle of rights, some positive and some negative, all of which require some action by society at large in order to have any meaning at all. Even those subdivisions themselves have subdivisions. For instance, the right not to be killed is essentially the right to life. The right to life is the right to defend that life. That right is itself meaningless without the right to use force to do that, and the right to use implements such as weapons to deliver that force, which itself entails the right to possess such implements.
Even that simple right to possess similarly entails the existence of such items, meaning that someone must have the right to manufacture them and to deliver them in interstate commerce. The assignment of the power to regulate interstate commerce in Congress not only states what they have the power to do but implies a responsibility to actually do it.
This even leads into implications in seemingly unrelated areas like taxation. For instance, if the government can't outright prohibit certain kinds of speech, can it punitively tax the means of delivering such speech to the point it makes it unprofitable or even impossible?
In any event, the terms "positive" and "negative" in this context have more similarity to the cognate of "positivism" than any attempt at propaganda, and it's actually usually libertarians who either claim positive rights, using that term, either don't exist or should be drastically curtailed. (I'd recommend Randy Barnett for a more academic analysis of these ideas.)
Okay, Deep Thoughts autismland or not, this is enough words to be tl;dr already so I'll finish.
Rather than go on about the liberty/right distinction, I'll just suggest that any positive liberty implies a negative right, i.e. freedom of speech implies a prohibition on government interference with the right. They are converse and congruent. Like this.
