Wily kindness is looking at your own experience without hostility, but also without blinders. With just the kindness, you often will lack the motivation or energy to actually get things done in your life. And with just the wily, you might be able to punch through the anxiety/depression, but underneath the hatred and struggle with, the lack of acceptance of, these states is causing you deep suffering.
I remember hearing an interview with an environmental activist who had been imprisoned in Arizona. She talked about the struggles of prison life, and about her own growth in the midst of it. The quote that has stuck with me for all these years is, "I've learned to love people who I cannot trust." The same could be said of skillful management of anxiety/depression, because the claims made by these states are deeply untrustworthy. And yet to hate them because of the ignorance of their claims is to jump right in with the roses--there's no winning that fight.
What are these claims? They usually go like, "The world is empty." "You're not worthy (of happiness, of love, of companionship, of grace, of joy)." "There is danger everywhere, so if you want to survive, be small!" "You can't possibly do..." "Be exposed and you'll be eaten." "No one loves you." "There's no way to solve your suffering." "It's all hopeless and you'd better just face it." Often they'll be phrased as "I...," but it's really anxiety and/or depression that is speaking, we just get confused about us not being the same as these states.
So with wily kindness, you practice recognizing that these messages are simply false (in the beginning, this takes faith on your part, and supports from others to help you believe this). But you also hold onto the fact that if you hate these states, because of this falseness, you are making more suffering for yourself.
This, admittedly, is a bit tricky, because if you've suffered with these states for a long time, particularly if beginning in childhood, then you've likely learned that the only thing keeping you from deep depression and anxiety is fighting them tooth and nail. But to move towards actually resolving and dissolving anxiety and depression, you have to learn to approach them with kindness, not animosity. Tall order? Only if you haven't yet experienced it. Once you really feel how different it is to sit with these states in watchful acceptance, and then act on them with the kind of attitude you'd take towards a beloved if wayward child, then it becomes clear how your strategy of struggle comes at a cost.
As an experiment (and an experimental attitude is extremely important in mastering these states), you can try the following exercise. (Though if you start getting overwhelmed, stop the exercise and do whatever is soothing to you. When you're overwhelmed, it's not only painful, but you can't really work. Be gentle).
1) Get physically comfortable.
2) Feel whatever depression/anxiety current is accompanying you (as thoughts, emotions, and physical sensations).
3) Start with the phrase, "Depression/anxiety, you are not my enemy," saying with as much conviction as you can find.
4) Notice if there are changes in your state (again, as thoughts, emotions, sensations).
5) Change the phrase and see if you can find something that feels truer. (For example, "Depression/anxiety, though you are difficult companions, I choose not to
6) Keep doing this till you find something that rings as believably as you're going to find (for some, it might be "I'm willing to consider that I'm not totally the same as these experiences...which suck!"--that's fine, as long as it's the truth for you).