Love comes in an infinite variety of flavors and shades, from simple human warmth to passionate adoration. To dance deeply, dance with love; connect with your partner. Dancing without love has its place, especially in the learning process, and a good dancer is always learning. But without love your dancing is superficial; to dance deeply, recognize your partner as a fellow human. What's important is your partner, and how you treat your partner. Compared to that, the history & traditions & rules etcetera of whatever dance you're doing are utterly trivial.
Fellow humans are equals, not superiors or inferiors; once you feel that shock of recognition, dominance and submission become inappropriate and naturally fade away. Equals collaborate, working and playing together; no one's in charge, no one's the boss. You may choose to play the roles of lead & follow, but you know it's just play-acting, just a game; you don't take it seriously.
At the deepest level, dancing can foster human evolution: transformational partner dancing. The key to making partner dancing evolutionary is to dance for your partner, not yourself. It's a universal principle: to grow, to get to any of the deeper & more fulfilling parts of life, you have to stop being selfish & self-centered. You have to get over yourself.
Whatever the 2 of you do is the dance, period. Nothing that happens is a mistake. Being a beginner, not knowing the dance - that's not a mistake, that means you're trying something new, which is a good thing. If you're not making "mistakes," if you're not goofing up on the dance floor, you're playing it too safe; you're stuck. You won't progress, with dance or anything else, unless you're willing to make mistakes, and continue to make 'em. Try something new, and be perfectly happy to fail spectacularly, then have a good laugh with your partner about it. Then go on dancing.
If one of you does something unexpected, intentionally or otherwise, that's part of your dance. The only mistake is reacting negatively to the unexpected. This is dancing, we do it for fun and joy; negativity has no place in it. Never get negative about the unexpected; run with it instead, play with it, make it work. Do everything you can to make the dancing work. Don't insist the dance be done "correctly," a certain way, and don't dance instructively, to help your partner improve. Correcting is poisonous and disrespectful, unless your partner specifically asks for it. Respect your partner, not dance traditions, correctness, or other mental constructs. Do everything you can to turn your partner's "mistakes" into fun, into unexpected adventures.
Respect is recognizing your partner as your absolute equal, in every regard, and feeling that way down deep in your guts. Dancers who are secretly insecure about their own dancing are often not-so-secretly disrespectful of their partners. Outmoded ideas about leading & following can undermine respect, e.g. the breathtakingly clueless catchphrase "Follows, are you doing your 49%?" Respect means absolute equality: nobody's in charge. If you need to be in charge, need for your partner to be in charge, or see your partner as anything other than your equal in every regard, that's a barrier to connecting.
The essence of respect is grasping the truth that another being cannot be greater or lesser than you. You can't think, wish or believe your way to that; you either see that it's true, or you don't get it yet. Respect is incompatible with unequal power sharing; if you want to control or boss your partner, or be controlled or bossed, you don't get it yet. Respect has nothing to do with fear, and it's nothing you can earn, because you don't deserve it. No one "deserves" respect; respect can only be given freely, as a gift. You can make someone fear you, but you have absolutely no influence over whether they respect you, i.e. acknowledge you directly from the heart; that's up to them, though you invite respect when you respect someone. And if you respect someone, you treat them kindly; respect and kindness are part of the same thing: open-heartedness.
Mutual respect is the starting point for going deeper into partner dancing. If you don't acknowledge your partner directly, and recognize him or her as your equal in every way, you can't go deeper; you'll stay on the surface. You'll just be going through the motions, like the fancy dancers with the frozen smiles you see on TV.
Connecting with your partner has nothing to do with how good a dancer you are. You can have mad skills & moves, and fabulous "dance connection," as they say in partner dance lingo, but as long as your attention's on you, you're not connecting. Connecting means being more interested in your partner than you are in yourself. Dancing that's focused on you - how you look, your pleasure, showing off your skills, working on your excellence - is disconnected dancing. Connected dancing is respectful, humane, egalitarian, kind and playful. Here are some things to consider if you want to connect:
Don't make dancing into work, into relentless striving for excellence. Let it be play instead; most of us have forgotten how to play. Real play is full of love, and your ability to play is a very good indicator of your relationship with love, with the life inside you. Our connection to the love that's inside, the love that doesn't depend on anyone else gets strangled as we grow up, it gets co-opted or trained or beaten out of us. We turn play into things like excelling at sports, crushing the competition, hardening & toughening ourselves for life's battles. We turn play into war or discipline or competition. All the love & joy get beaten out, and what we're left with is "play" that's just another chore, or a way to get a competitive advantage, or something to beat yourself up over. Same old crap. Partner dancing can be a way to reconnect with real play, with joy, which is love spilling out of you.