I want to discuss this phrase.
To start, let's look at the first part, "God gives us". This tells me that God has given me this situation. So when you say this to me, you are saying that God has placed that tumor in my child's head. God gave me a sick child. God is the reason that my child has cancer.
If I were not a believer in God, I'm not sure that would make me very interested in learning more about Him.
Then, let's look at the second part, "what we can handle". I assure you, I cannot handle this. This mass in my daughter's head wasn't placed there because God knew that I could handle it. I'm not any more equipped to handle it than you or anyone else.
Again, if I were not a believer, I would think that God obviously does not know me very well if He thinks this is something that I can handle.
Now, let's look at what the Scriptures say about troubles.
The Lord is a refuge for the oppressed,
a stronghold in times of trouble. Psalm 9:9
Though I walk in the midst of trouble,
you preserve my life;
you stretch out your hand against the anger of my foes,
with your right hand you save me. Psalm 138:7
In this world, you will have trouble. But take heart! I have overcome the world. John 16:33
Praise be to the God and Father of our Lord Jesus Christ, the Father of compassion and the God of all comfort, who comforts us in all our troubles, so that we can comfort those in any trouble with the comfort we ourselves have received from God. 2 Corinthians 1:3-4
These verses tell us that we will face troubles. Hard times will come. Not that He will send them, but that they are there. The verses also say that God is our stronghold, He saves us, He has overcome the world, and He will comfort us. It isn't about what we can handle but what He can handle alongside us.
Perhaps, instead of "God only gives us what we can handle." what should be said is, "God helps us handle what we are given."