"God won't give you more than you can handle."
The idea comes from First Corinthians 10:13 which says, "No temptation has overtaken you but such as is common to man; and God is faithful, who will not allow you to be tempted beyond what you are able, but with the temptation will provide the way of escape also, so that you will be able to endure it."
Did you see anything in there about hard times? About trials? About suffering or persecution? This verse is talking about temptation. God is promising that every temptation we encounter has been faced before. It is not unique to us, even though in the midst of it we feel as though it is. He is promising that as powerful as the temptation to sin may be in the moment, He is more powerful. If we belong to Him, then His Spirit in us can enable us to overcome that temptation and not give in.
He also promises a way of escape from the relentless obsession that temptation can often be. But notice too, that He does not promise to completely removed the temptation. He will not treat us like babies in a playpen, removing any possibility of us getting into mischief. The power He gives us will enable us to endure the temptation without giving in to it, even while it still taunts us.
Many times we have to face more than we can handle. Life is set up that way. If we could handle it all by ourselves, we wouldn't need God. Sorrows, heartaches, trouble, and disease are often more than we can handle. Life threw us a curve ball and we weren't ready.
"God won't give you more than you can handle" actually does more to incite anger toward God than to bring comfort. Even as it is being said, our hearts want to scream, "Well, this time it IS more than I can handle!" This catchy phrase portrays God as a trickster who keeps adding burdens to our backs just to see how much we can handle. He gleefully adds one more disaster and steps back to see if we will crack. That is not God.
The true God suffers when we do. He walks with us through the valleys, holds our hand, and whispers His encouragement, "Fear not. I am with you." He knows life is more than we can handle, so He does it with us. And because death is more than any of us can handle, He prepares an eternal home for us and provides the way for us to get there.
Rather than repeat this inaccurate phrase, let's say instead: "I know this feels like more than you can handle, but God is with you. He will strengthen you and comfort you and bring you through it. He cares about you. You can trust Him with this."