Bart Ehrman harps on Mk 1:41. He uses that as a showcase example to demonstrate the allegedly problematic state of the NT text. Consider two translations representing the two different variants:
Jesus was indignant. He reached out his hand and touched the man. "I am willing," he said. "Be clean!" (NIV).
Moved with pity, he stretched out his hand and touched him and said to him, “I will; be clean” (ESV).
i) Was Jesus "moved with anger" or "moved with pity"? A number of scholars think this verse presents a text-critical dilemma, because the two rival readings confront us with conflicting textual criteria. On the one hand, the "compassionate" reading enjoys far stronger external attestation. On the other hand, it's hard to see what would prompt a scribe to intentionally change the original from "moved with pity" to "moved with anger". So internal grounds favor the "indigent" reading.
Keep on mind that on this view, it's only a dilemma if the scribal variation was intentional.
ii) Peter Williams thinks this was an accidental scribal error:
If his explanation is correct, that would dissolve the dilemma. An unintentional mistranscription would be consistent with the external attestation. Indeed, if this was an unusual, but accidental mistake, then it's unsurprising that it wasn't more widely disseminated in the MSS record, inasmuch as few scribes would independently repeat that kind of mistake in that particular location.
iii) Other textual critics propose a different explanation. See the ensuing discussion in the Evangelical Textual Criticism post I linked to.
iv) In that event, we don't have to puzzle over why Jesus was angry, since that's not the original reading.
v) But suppose, for the sake of argument, that we think the "indignant" variation represents the original. On the face of it, it's perplexing that Jesus would get mad at a leper who approached him for healing.
Mind you, it's easy to speculate. Suppose a serial killer developed Parkinson's disease, and sought out Jesus for healing. Jesus knows something about his double life that the reader does not. And it's understandable that Jesus would take umbrage at the prospect of healing an evildoer like that. So there's nothing inherently inexplicable about the notion that Jesus would irate about a certain kind of person who came to him for healing. His disapproval would be based on his divine insight into the character of the supplicant. But the reader isn't privy to that information.
However, that conjecture fails to explain why Jesus complied with the leper's request despite his disapproval.
vi) Another explanation is that Jesus is not indigent at the leaper, but his condition. Jesus is outraged by the suffering itself.
vii) But whichever reading is original, that's consistent with Markan Christology, Synoptic Christology, and NT Christology generally. Our doctrine of Christ doesn't hinge on which reading is original in Mk 1:41. We needn't revise it depending on which reading is original. At worst, it means we can't read Christ's mind. We don't always understand what motivated his actions. But that's realistic.