The conclusion is the first sentence. The verb "promotes" is causal. We are talking about whether democracy as a political system promotes political freedom (i.e., whether it causes there to be more political freedom) in general.
Step back for a second and think about what it means to say A promotes B in general (as opposed to a specific A and a specific B). For example, exercise promotes good health (as opposed to Joe's exercising promoting his good health). Again, it's pretty obvious that we're talking about causation. But what does "causation" mean here?
Does it mean that A is sufficient for B? No. Because "exercise is sufficient for good health" is false but "exercise promotes good health" is true. Plenty of people exercise and are not in good health. In fact, their poor state of health may be why they're exercising - they're trying to improve their health. And plenty of other people exercise to the detriment of their health. They overdo it, hurt themselves, or worse. But it's still true that "exercise promotes good health."
Does it mean that A is necessary for B? No. Because "exercise is necessary for good health" is also false. Plenty of people don't exercise yet are perfectly healthy. Maybe they have great genes, a healthy diet, or they're just young. There could be a number of reasons. But it's still true that "exercise promotes good health."
The point is that a causal claim like "A promotes B" doesn't mean that A is sufficient for B nor does it mean that A is necessary for B. Because that's just not how causation works in the world. Causes tend to be partial. They tend to exert their causal power along with other causal forces. Exercise in fact is a causal component for good health but there are many other causal components (genes, diet, age, preventative medicine, not getting hit by a bus, etc.). They all work together to produce the effect.
This is the confusion at the heart of the argument. The "political scientist's" conclusion is a causal claim but she confused it for a bi-conditional claim.
Let's help her out. Let's swap out her causal conclusion with a bi-conditional conclusion: It's not the case that political freedom is promoted if and only if the political system is a democracy.
If we don't touch the rest of her argument, then she's all set. Premise one "democracies that suppress political freedom" proves that democracy isn't sufficient. Premise two "autocracies that promote political freedom" proves that democracy isn't necessary. Done!
So another way that the correct answer could have been worded is perhaps something like this: The reasoning in the political scientist's argument is flawed because it confuses a causal claim with a conditional claim.
But if you scratch that a bit and ask "Why is it a reasoning flaw to confuse a causal claim with a conditional claim," well, stroll right on over to (D). It's a flaw because in general, a cause can be a cause without being either sufficient nor necessary. Democracy can be a promote political freedom without being sufficient nor necessary for political freedom.
All of the above is with the caveat that we're talking about general phenomena, which is what this question is about. If instead you want to talk about specific phenomena, like Joe's rainy weekend rock climbing accident causing his extra-articular wrist fracture, then his rock climbing is a necessary condition. Had he not gone rock climbing, then his wrist wouldn't have broken in that exact way. But his rock climbing still isn't sufficient since all other causal forces had to conspire, e.g. the rain had to have fallen in order to make the rock slippery in the first place.