There is no single MIT licence, and the FSF advises against using the term as it is ambiguous. Assuming you're referring to the X11 licence, which seems to be the most common one so named, the licence obligation is that
The above copyright notice and this permission notice shall be
included in all copies or substantial portions of the Software.
According to choose-a-license, to apply this licence you should
Create a text file (typically named LICENSE or LICENSE.txt) in the root of your source code and copy the text of the license into the file. Replace [year] with the current year and [fullname] with the name (or names) of the copyright holders.
There is no obligation on you to make your software disgorge the licence terms, or the licence itself, in response to any particular command-line input; you just have to include the copyright and permissions statements somewhere in what you distribute.
But if, in order to keep what you distribute down to a single binary, you were to choose to make your software behave so, then as Brandin notes above, the most common flags would be
owned by is fairly confusing language, so stick with
Library X (c) Fred Yoyodyne, 2018). If you were to make your software, in response to the chosen flag, disgorge the relevant copyright statements along with the full text of the licence, that would fulfil your obligations, it seems to me (caveat: IANAL/IANYL), as "embedded in the binary" is one way to satisfy "included".
If you're distributing more than just a binary (eg, because you're using a package manager to distribute it), then include the relevant file, and don't worry about getting the binary to disgorge anything licence-related.