This RFC was the result of a long discussion that took place in many forums over the course of several years, so it's tricky to summarize. Here's my attempt:
1. Memory safety is Rust's number one priority, and if this were a memory safety concern then Rust's hands would be tied and it would be forced to use checked arithmetic just as it is forced to use checked indexing. However, due to a combination of all of Rust's other safety mechanisms, integer overflow can't result in memory unsafety (because if it could, then that would mean that there exists some integer value that can be used directly to cause memory unsafety, and that would be considered a bug that needs to be fixed anyway).
2. However, integer overflow is still obviously a significant cause of semantic errors, so checked ops are desirable due to helping assure the correctness of your programs. All else equal, having checked ops by default would be a good idea.
3. However however, performance is Rust's next highest priority after safety, and the results of using checked operations by default are maddeningly inconclusive. For some workloads they are no more than timing noise; for other workloads they can effectively halve performance due to causing cascading optimization failures in the backend. Accusations of faulty methodology are thrown around and the phrase "unrepresentative workload" has its day in the sun.
4. So ultimately a compromise is required, a new knob to fiddle with, as is so often the case with systems programming languages where there's nobody left to pass the buck to (and you at last empathize with how C++ got to be the way it is today). And there's a million different ways to design the knob (check only within this scope, check only when using this operator, check only when using this type, check only when using this compiler flag). In Rust's case, it already had a feature called "debug assertions" which are special assertions that can be toggled on and off with a compiler flag (and typically only enabled while debugging), so in lieu of adding any new features to the language it simply made arithmetic ops use debug assertions to check for overflow.
So in today's Rust, if you compile using Cargo, by default you will build a "debug" binary which enables checked arithmetic. If you pass Cargo the `--release` flag, in addition to turning on optimizations it will disable debug assertions and hence disable checked arithmetic. (Though as I say repeatedly elsewhere, Rust reserves the right to make arithmetic unconditionally checked in the future if someone can convincingly prove that their performance impact is small enough to tolerate.)