Deer Park Monastery, Escondido, CA
Thich Nhat Hanh has written quite a lot of books and gives many Dharma talks, maybe at least once a week. Most of the time, they are variations on core central themes, which are quite expansive and allow him to give talks so often without constantly repeating himself. But he does repeat certain ideas over and over again.

A recurring teaching that his followers seem to enjoy repeating and relating is that when you have a negative thought or feeling that your natural reaction is to push away or run away from, you should instead embrace it like a baby, imagine cradling it and saying to it, "There, there little negative emotion, I will pay attention to you and attend to you". Then they hold their arms like they're holding a baby, and caress an imaginary negative emotion. It's enough to making me scream. They don't explain it any further than that, they just repeat the teaching. And cradle their arms and caress. Cult.

Maybe they get it. I think I get it in my own way which might be different from theirs. But if I ever did relate this teaching to someone else, like you, I would make sure I explained my interpretation of the teaching.

Explanation of my Interpretation of the Teaching:
It actually hit me yesterday what it meant to me. Taking something negative or painful and embracing it (without the arm gestures, thank you) means bringing it close and being intimate with it, first and foremost to detach it from anything outside of you that you might blame for causing the feeling. You take ownership and responsibility for your own feelings, and if you're too busy blaming someone else for causing them, you can't effectively process them in a healthy, productive way. Just concentrate on the feeling itself that you're causing, you're generating and don't think that something apart from you is causing the feeling.

That's just the starting point. It's not meant to solve the problem. That's how you start dealing with the real source of the negative feeling. Maybe you can meditate on the emotion, focus on it and concentrate on it and transform it. Maybe you can analyze it psychologically to understand it or yourself better. Maybe you can think about it practically to formulate some sort of solution. Maybe it doesn't do anything and goes no where and sits there for a year like fruitcake, at least you're not exacerbating and perpetuating it by blaming someone else for your feeling (I seem to enjoy bolding that word).

Embracing the negative feeling is a meditation right away because it takes effort to rein it in and not go reacting to it, expressing anger or blame. You have to concentrate to calm down, maintaining mindful breathing, and bringing it close to you and refuse to blame someone else for your feeling. I don't know, it all may seem theoretical. Most people can't be bothered, I suppose.