Because that’s how the linking algorithm used by GNU linker works (a least when it comes to linking static libraries). The linker is a single pass linker and it does not revisit libraries once they have been seen.
A library is a collection (an archive) of object files. When you add a library using the -l option, the linker does not unconditionally take all object files from the library. It only takes those object files that are currently needed, i.e. files that resolve some currently unresolved (pending) symbols. After that, the linker completely forgets about that library.
The list of pending symbols is continuously maintained by the linker as the linker processes input object files, one after another from left to right. As it processes each object file, some symbols get resolved and removed from the list, other newly discovered unresolved symbols get added to the list.
So, if you included some library by using -l, the linker uses that library to resolve as many currently pending symbols as it can, and then completely forgets about that library. If it later suddenly discovers that it now needs some additional object file(s) from that library, the linker will not “return” to that library to retrieve those additional object files. It is already too late.
For this reason, it is always a good idea to use -l option late in the linker’s command line, so that by the time the linker gets to that -l it can reliably determine which object files it needs and which it doesn’t need. Placing the -l option as the very first parameter to the linker generally makes no sense at all: at the very beginning the list of pending symbols is empty (or, more precisely, consists of single symbol main), meaning that the linker will not take anything from the library at all.
In your case, your object file example.o contains references to symbols ud_init, ud_set_input_file etc. The linker should receive that object file first. It will add these symbols to the list of pending symbols. After that you can use -l option to add the your library: -ludis86. The linker will search your library and take everything from it that resolves those pending symbols.
If you place the -ludis86 option first in the command line, the linker will effectively ignore your library, since at the beginning it does not know that it will need ud_init, ud_set_input_file etc. Later, when processing example.o it will discover these symbols and add them to the pending symbol list. But these symbols will remain unresolved to the end, since -ludis86 was already processed (and effectively ignored).
Sometimes, when two (or more) libraries refer to each other in circular fashion, one might even need to use the -l option twice with the same library, to give linker two chances to retrieve the necessary object files from that library.