I have only learned since (recently) beginning to study Zen [that one can sit with one's problems]. Before, I had the notion that problems must be gotten rid of in order to be happy. Now I am understanding that when I sit, I sit with things, problems included. I will try to view my circumstances with gratefulness at having to learn these lessons.
Sitting with our problems and negative emotions often removes much of the fuel which fires them, for there is a vast difference between, for example, merely observing and experiencing and "being with" our feelings of anger or sadness vs. wallowing in our anger and sadness, stoking them up, fanning them and letting them take us over, obsess us and dominate our thoughts. Let the waves of emotion just roll on through (even if they feel like they will crash over you sometimes, even sweep you away. Let them roll on through like a passing wave on the sea).
... This lets us observe dispassionately the aspects of our problems and emotions which are, in so many ways, but mind created theatre of our own making... sometimes comedy, sometimes drama ... passing clouds of thought, the changing weather of mood and circumstance. In some important ways, our lives are like stories on the tv ... and we can change the channel!
In many cases, doing so lets us replace the seeds of harmful emotions with positive, healthful and helpful emotions ... anger replaced with peace and loving kindness, resistance made into acceptance, greed turned into charity etc. etc.
Now, that does not mean that sometimes we will not still be taken over by greed, anger and ignorance ... on some days the anger and sadness will still get us.* (Even "Zen Masters" can fall into depression and such at times in life). We are human beings, not saints. Some days, we still need to vent, have a good cry. Some days may actually need and deserve it! But overall, we will not be prisoners of these thoughts and emotions, trapped by them and unable to see things a different way.
Our Buddhist Practice allows us those other ways of seeing and living.