If people are getting that statement confused with 1 Corinthians 10:12-13, which states "So, if you think you are standing firm, don't fall! No temptation has seized you except what is common to man. And God is faithful; He will not let be tempted beyond what you can bear. But when you are tempted, He will also provide a way out so that you can stand up under it," we must be careful to consider what Paul is referring to in this Scripture. He is referring to temptation and sin. The verse states that no temptation can overtake us unless we choose to let it. God's promise here is that He will always provide a way out of temptation so that we don't have to sin; we just have to seek His way out. Making the choice to take God's escape route when faced with temptation makes us more like Him.
On the other hand, some people might mean that with God's help, we can face and handle anything that comes our way, no matter how rough, tough, or fierce it is. No matter how hard the battle is, no matter how severely the storm rages, with God's help, we can and will overcome it. The problem with stating that fact through the words "God will not give us more than we can handle" is that it could cause people to start to doubt God's faithfulness when they're in the midst of a storm they really feel they cannot handle. It can cause people to turn away from the living and true God because we start to ask the question, "I thought you said God would never give me more than I could handle? Well, I CAN'T handle this. I'm not strong enough!" When we are in a storm that shakes our world, that turns it upside down, and shakes the entire foundation of our lives, we really don't feel that we can handle it. And we CAN'T! That's why we need God's strength to get through it. God will give us trials that we can't face alone; those are there to draw us closer to God and to rely on Him when we literally cannot see the next step in front of us (James 1:2-4). When we have no idea which way to go or where we're going to get the strength to move, that's the PERFECT time to rely on God. He is faithful; He is faithful through the good and tough times. He has already won the battle, and if we are His followers, we have already won, too!
When my husband and I decided to step out on faith to follow God's leading me to be a stay-at-home mom, we had no idea where the money would come from. We did not see an answer; we did not see the provision, but that's where faith came in. It's not faith if we already have the answer. We must put our faith in God 100% and trust Him when he asks us to step, leap, or dive forward. We put our faith in Him and wait on His timing to provide just what we need right when we need it. We will question things, such as situations and outcomes. It's sort of natural to do that. I know I am selfish by nature, so when I question God about why a certain situation or outcome occurs, it's because I am miserable or am experiencing discomfort. His plan is perfect and I just have to continue to trust in His promises!