Another classic is the “joins are slow” argument, which I believe goes back to a period in the late 1990s when in one, not highly regarded at the time, database, namely MySQL, they were indeed slow. But the reason “everyone” knew about this was precisely the oddness of this situation: in fact RDBMSes are highly optimized pieces of software that are especially good at combining sets of data. Much better than ORMs, anyway, or, god forbid, whatever you cobble together on your own.
There is, in my mind, only one valid reason to not use foreign keys in a database schema. If your database is mostly write only, the additional overhead of generating the indexes for the foreign keys may slow you down a little (for reading, these very same foreign keys in fact speed things up quite considerably). Even in such a case, however, I’d argue you’re doing it wrong and there should be a cache of some sort before things are written out in bulk to a properly setup RDBMS.