Also, it can also be a plan to rush to a MVP, rewrite the MVP in your language and go from there. This has the added benefit of giving you a decent sized program in your language at no extra cost - aside from testing this should make you design a better language as you learn what works at what doesn't in the "real world".
It's not always possible (Please don't write a compiler in Javascript, or even C if possible - pain and lack of abstraction respectively).
As for the parser, it's probably true that for many languages, self-hosting the frontend may be attractive. For others it might not. Someone else wrote: "if people who are really good (let's say) Go programmers want to make the Go compiler better they then don't have to try and write go in C++ if the main compiler is written in C++", which is somewhat true. On the other hand I once had to do stuff in the gfortran frontend, and I was very happy that it was written in C and not Fortran, because I know C but don't know Fortran. So I guess as long as your language is niche among people likely to be compiler developers, the point about attracting that talent doesn't hold. If your language gets popular enough, self hosting the frontend should become more interesting. Before that it's more of a gimmick.
Not necessary at the beginning, but eventually as the language gains mindshare.
It is very hard to understand the language, if all contributions to improving it are done in another language.
Somehow it is similar to being a library author without having ever written a full blown application using the library, thus being blind to what are the possible usability issues.