In order to get a solid handle on a proposal, it isn't enough to just know what the world will look like if you adopt the proposal. It is also very important to know what the current situation or counter-model is, otherwise the proposal may provide less of a benefit than expected. Before I begin, I'll note that this article is about the comparative, I'll write another article for being comparative later, though probably under the name being responsive since this will be less confusing.
One of the best ways to think about what it means to be comparative is that you want to indicate what the two worlds will look like. For example, conscription may provide us with more troops and everyone might agree that troops are important for winning wars, but we also need to look at what the status quo is like. If the country already has enough troops or allies, then the difference in the comparative might not be that significant. When we ignore the comparative, we can often get caught up in a particular frame and fail to realise that the framing is misleading. At first, being able to better win wars might sound like it is really, really important. But when we ask the question of whether or not we need to be better at winning or if we are good enough, we might quickly realise that it doesn't really matter. As can be seen here, there is no need to wait for the other team to bring arguments before you can start being comparative.
Here the first speaker in, This house supports nationalism, provides a good example of being comparative. He explains that he doesn't see the comparative as being some utopian cosmopolitan society, but that people will always choose a particular form of identity. He say that this should be nationalism; not ethno-nationalism, but rather a form of nationalism based on shared values. He argues that this is advantageous since everyone in a nation can opt into this identity and hence it avoids the divisions that occur when people opt into specific identities such as race or gender. The speaker also talks about how nationalism can energise the nation, but if the speaker had only talked about this, then the argument would have been weaker. In this case, thinking about what the world would otherwise look like allows you to make nationalism more attractive since we can see that the alternatives are not particularly compelling.
As another example, consider a debate about banning abortion. Imagine that the government stands up and talks about why they think the fetus is a person and hence it should be illegitimate to abort it. However, their argument will not be as persuasive if they fail to deal with the comparative, which is that many women will get abortions whether or not it is legal and these abortions will be more dangerous. In this debate, the comparative weakens the affirmative case, but it also allows the government to pre-emptively respond to this point. This objection is also common knowledge, so unless this is responded to, this analysis will likely be rejected outright.
So, as we have seen, being comparative allows you to be more persuasive and to think in a more nuanced manner about an issue. It provides the language to explain to a friendly argumentation opponent how you think their argument could be improved or why you don't think that their argument is very persuasive.