Balance is the crux of life. Everything in life is in perfect balance and harmony. The night balances the day, the good balances the bad and so on. Even in atoms that are the very building blocks of the physical universe, there exists a positive charge (protons) that is balanced by the negative charge (electrons).
In this quote, Rumi is right in saying that life is a balance between letting go and holding on. There is a time to hold on and then there comes a time to let go and release.
The very act of releasing is powerful – it leads to healing, it helps recharge your energy and put things into perspective.
In-fact, most of the times these things happen naturally. When you become tired of holding on, you naturally have a tendency to let go. When you let go, all that energy that got drained from you while holding on starts to replenish. You start to feel renewed to the point where you get encouraged to take action again. In this way, letting go helps you gain clarity so you can pursue things that really matter.
So do not feel guilty to let go for that is inevitable and for the greater good.