Disadvantages

Let's face it. Brainfuck is esoteric language. It was created as a joke, and conforming to author's will is recommended. There are many so-called Brainfuck hackers around, but being honest, You can't earn a living programming in Brainfuck.

Brainfuck is too impractical to be using language in real-world cases. Developers would cost way too much and work really inefficiently. Albeit low abstraction level, Brainfuck is memory and CPU time inefficient (a bit like JavaScript on web), so it's not very viable to write anything in bare Brainfuck and you'd be better off by using some kind of Brainfuck assembler, or HLL to brainfuck compiler, but none of the listed can beat pure C implementation instead of Brainfuck one.

Finally, the language is a bit constrained - I/O is limited to console input and output, greatly reducing use cases.