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Because you want to persuade them? When you speak someone's language, using similar posture, vocabulary, style, and being attentive and tuned into them, they're more likely to react positively and buy what you're selling.

http://lifehacker.com/5894462/use-mirroring-and-matching-to-...

That's stupid advice. Why should I always match my tempo to somebody else?

Because it's an important element of building rapport. And rapport is important if you want to get someone on "your side" in a discussion.

for the same reason that you're probably not going to try to match mine

But people usually do just that. It's a fairly well established thing, that people in a conversation usually eventually match each other's talking pace. And it generally feels awkward when you're talking to someone and that doesn't happen.

The word "should" is ambiguous. Here it doesn't mean some kind of moral duty, but just that you'll generally have better results.