Allows you to disagree with someone while making it hard for them to disagree back, because you also agreed.
Doublespeak usually doesn't get responded to in my experience because it's so difficult to counter well. It makes most people (myself included) feel very uncertain in responding to it, so often it can be a sort of free win all on its own.
If you say you agree with me, you lose, because you're agreeing with statements that contradicted your position, and if you say you disagree, I can react by ignoring the parts in my post that disagreed with you and acting like I was just agreeing and you responded by still disagreeing with me, so you're obviously just a troll looking for an argument.
Against doublespeak, you have to structure your response carefully to agree and disagree to parts of something within the same post, while paying attention to the overall tone you're forming. You don't want to, for example, come off as if you think a position very close to yours is equally wrong as a complete antithesis - that makes others see you as unreasonable and intolerant.
One technique I find useful in countering it is fake uncertainty. Even if you know exactly what's going on, phrase the response like, "I'm a bit confused by your post. Do you mean (the thing you agree with)? If so, then I must be misunderstanding what you said about (the contradictory thing)".
Example time. Back in my Spellweaver days, I read a thread on the forums (I wasn't a participator in this one) that ended up an argument more or less about communism. Two posters were discussing a hypothetical about an island where one person out of many had all the coconuts, and there was no other food, but it was because only this person was doing the picking. One poster rightly pointed out that if the other islanders want any coconuts, they should pick their own.
The person who was clearly in the wrong and losing the argument resorted to: "I'm happy to help pick them, but you'd better be sharing."
See the doublespeak? If he's picking them too, then it's not sharing because he'd have his own. The good-faith options were to admit either that he isn't entitled to someone else's labor if he's unwilling to work to support himself, or that he thinks others should be forced to provide for him even if he could and chooses not to provide for himself.
The only way his statement would make sense is if only this one person possessed the means to pick coconuts and refused to let others use the equipment in return even if they offered compensation. (In that circumstance, I would make an exception to libertarianism and condone stealing the means to pick coconuts.) But that wasn't part of the scenario at all. He resorted to doublespeak because it was that or admit his argument made no sense.
A related thing is when someone downgrades your statement, but frames it as an agreement. For example, I saw a Backalley Philosophy video explaining how democracy is a nonsensical ideology of nihilism and no rights for anyone and there was a comment saying something like, "I agree! Democracy is a form of light tyranny!". The video argued that it was a form of tyranny no less extreme than monarchy, so if you only think it's light then you're not exactly agreeing, are you?
This trick can be used to disagree with an extreme but correct statement while escaping the expectation of giving a reason for disagreement.