All perfect praise be to Allaah, The Lord of the Worlds. I testify that there is none worthy of worship except Allaah, and that Muhammad is His slave and Messenger.
There is no harm in describing a person as self-sufficient and in no need of others', i.e. able to dispense with other people. In fact, this is the meaning that comes to one's mind when hearing this description.
However, if the intended meaning is that the person can dispense with everyone including his Lord as well, then this is impermissible and unacceptable. Verily, all people are in need of Allaah, The Exalted, and can never dispense with Him. Allaah, The Exalted, says (what means): {O mankind, you are those in need of Allaah, while Allaah is the Free of need, the Praiseworthy.}[Quran 35:15] Indeed, people are always in need of Allaah, The Exalted, and can never do without Him or dispense with Him even for the blink of an eye.
Anyway, one does not intend this (impermissible) meaning when uttering this phrase, so there is no harm in uttering it.
Allaah Knows best.