I've read these sentences several times, but I didn't really understand it. The translation bot didn't provide any clarity either. Therefore, I think the lack of understanding is due to our different experiences, not to language peculiarities.
I can elaborate/clarify.
Partner dance is an intensely personal activity, where personality compatibility matters. For someone you only connect with through social dancing, this is not terribly difficult--the pair can present their most easily palatable face, and ignore any lingering incompatible traits of their partner for the duration of the dance. For someone you interact with more regularly, this is a bit more challenging, because the time spent together results in a familiarity where it is difficult to present only the facets of yourself that are acceptable to your partner. Because of this, it seems logical that the best possible dance partner would be someone you are already personally close to and have already found deep compatibility. Spouses and significant others seem like they ought to be the very best choices.
But that turns out to be almost exactly inverted from how things play out in reality. Partner dance has quite specific requirements for each role to work well--requirements massively different from the roles (most) people play in everyday life. So when we dance regularly with a SO, we need to negotiate two totally distinct sets of rules for how the relationship works; one for the floor, and one for everywhere else. That requires a significant amount of self-awareness and interpersonal negotiation...and even more importantly, the ability to sharply compartmentalize the two domains.
Most people aren't prepared to do that. Certainly not when dance (or the personal relationship) is relatively new to them. So when things go wrong on the dance floor, you see significant bleed-over from issues in the personal relationship (e.g: "The stupid way you execute that step even when I correct you is sooooo obviously connected to the way you refuse to listen to me about how to feed the baby properly!"). It manifests outwardly as a rocky dance relationship, but the problem isn't actually the dance.
We see a lot of examples of this in our dance studio. One popular element of our business is helping folks design, practice, and perform a First Dance for their wedding. And as terrible as it is to say, you really can tell which marriages are going to be difficult just by observing how the couple relate to one another as dancers. Reiterating and restating what I said in the short statement you quoted: dance partnership can and will expose every point of personal friction, even ones thought to be carefully hidden.
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On the other hand, the reverse direction seems to work just fine. Selecting a personal partner from the set of one's highly-compatible dance partners is no less successful than the usual run of relationship-finding. The worst incompatibilities and insecurities are clearly on display from the very beginning!