It makes sense that if you're designing a language, you'd like the language you made and would want to use it. It's fine for compilers like that to exist, and even be the main one used, but ideally it shouldn't be the only compiler.

But there are technically ways to bootstrap a language without writing it in another language (other than a small core in assembly or something). You could design a tiny compiler that only handles a small subset of your language, then write a better compiler using only the features available in that subset. You can do this for several layers of compilers until you have the full language.