"God doesn't always heal."
I think these words are meant to convey that Christians should seek the will of God, as we don't know if he's allowing illness for some purpose that's ultimately for the believer's good. Or perhaps these words are meant to remind us that we aren't entitled to blessings or in any position to demand them from God.
A similar, well-intentioned statement is: "Our greatest spiritual growth comes through trials." This is probably meant to remind us that trials cause us to run to God and may reveal a complacent heart.
Indeed, these are important lessons for the believer to reflect on when life is going well. But such statements may be deeply harmful when made to those who are struggling through an illness or difficult life circumstances.
That's because even strong Christians may be tempted to doubt God's love at times when they're overwhelmed by physical or emotional pain. Hearing "God doesn't always heal" might cause a person to focus on the idea that she's the exception—and then question, Why doesn't God want to heal me? Am I less important to God, or less worthy than others?
In this way, these statements may paint an ugly picture of God as preferential, or indifferent, or harsh—like a drill sergeant who uses only extreme methods to whip us into shape, and who favors the strong.
There's a truer statement to be made that reflects God's love for us: God always heals. Whether it's through temporary healing provided in this present life, or in the complete physical and emotional healing that he will provide in eternity (Revelation 21:4), God heals all wounds.
God's Daily Care
Consider how God heals us physically, in this present life, the vast majority of the time. Think about all the times you've had colds, headaches, back pain, an upset stomach, and cuts and bruises. These didn't just go away—each time the illness or pain passed because God provided healing, both through his design of the body and by his hand (James 1:17). God's design of our physical body tells us something profound about God: He cares so deeply about our pain that he built in a system of healing.
Further, most of us are relatively healthy, most of the time. Although it may be easy to recall lengthy or painful illnesses, it's impossible for most folks to count the number of days they've been well—there are just too many. This should remind us that God is caring for us on a daily basis.
I've observed a surprising trait among Christians who suffer from chronic illness or disability: They overflow with joy and demonstrate faith in a measure that isn't typically found among the healthy. How is this possible? Pain certainly isn't the impetus for rejoicing. This is surely a result of a felt abundant provision from God.
With this in mind, it seems our greatest spiritual growth isn't from a trial itself—it's not pain that makes us spiritually stronger. Rather, our growth comes through God's provision when we're experiencing trials. When we witness his love, comfort, and healing, we learn experientially and relationally about who God is.
Health and healing show us that God is relational, aware of our needs, and that he's the provider of every good thing. These blessings testify to us about God's character—and remind us that we are known and loved.