This was the exact wording of a test question given by my biology teacher and she said that white matter would repair faster, because there is a myelin sheath to protect the cells.
Do you agree with this answer? Could you give me a more detailed, real life (not school, but real neuroscience, real data) explanation?
Short answer
As @BryanKrause indicates, neither answer really makes sense.
Background
This is basically per the answer of @BryanKrause. Myelin is the stuff that forms the main characteristic component of white matter. White matter being
[the tissue] found in the deeper [in] the brain (subcortical). It contains nerve fibers (axons), which are extensions of nerve cells (neurons). Many of these nerve fibers are surrounded by a type of sheath or covering called myelin. Myelin gives the white matter its color. It also protects the nerve fibers from injury. Also, it improves the speed and transmission of electrical nerve signals
I think what the question aimed to target was your understanding what a myelin sheath is for (and, hence, what it is not intended for). Quoting from (Morell & Quarles, 1999):
[A] greatly extended and modified plasma membrane wrapped around the nerve axon in a spiral fashion. [It] originates from and are a part of the Schwann cells in the peripheral nervous system (PNS) and the oligodendroglial cells in the central nervous system (CNS)
Each myelin-generating cell furnishes myelin for only one segment of any given axon. The periodic interruptions where short portions of the axon are left uncovered by myelin are the nodes of Ranvier, and they are critical to the functioning of myelin.
In myelinated axons, the excitable axonal membrane is exposed to the extracellular space only at the nodes of Ranvier; this is the location of sodium channels. When the membrane at the node is excited, the local circuit generated cannot flow through the high-resistance sheath and, therefore, flows out through and depolarizes the membrane at the next node, which might be 1 mm or farther away []. The low capacitance of the sheath means that little energy is required to depolarize the remaining membrane between the nodes, which results in local circuit spreading at an increased speed. Active excitation of the axonal membrane jumps from node to node; this form of impulse propagation is called saltatory conduction (Latin saltare, “to jump”). Such movement of the wave of depolarization is much more rapid than in unmyelinated fibers. Furthermore, because only the nodes of Ranvier are excited during conduction in myelinated fibers, Na+ flux into the nerve is much less than in unmyelinated fibers, where the entire membrane is involved.
Your biology teacher's question is unfortunately poorly formulated and the justification is even worse, not just biologically but also logically. For the logical error, consider this statement: Knights wearing chain mail heal faster because they are protected by their armor. This makes no sense. Perhaps if you allow that the initial damage is less, but even that makes little sense.
It doesn't really make much sense to talk about healing speed of white matter and grey matter because you are talking about two different things. White matter is mostly axons and their myelin sheets, whereas grey matter consists of cell bodies and neuropil. Grey matter damage implies cellular death. White matter damage implies loss of connectivity. Grey matter damage can also lead to white matter degradation (i.e., the cells that sent projections are now dead). White matter damage can also lead to grey matter degradation due to loss of connectivity.
However, it is true that different types of brain injury could differentially impact white versus gray matter, but going into all the different causes of brain injury is too broad of a topic for a single question at stack exchange.
Furthermore, repair of CNS tissue is just as much about compensation rather than repair per se. Repair processes are important for limiting damage, cleaning out dead tissue, and restoring some types of connectivity, but recovery from a major injury is just as much about brain plasticity and effectively relearning how to function after an insult.
