There is no contradiction. The question is simply not a proper one according to general relativity which self-consistently described both of these physical systems. Have a look at a few other answers I have already given on this:
The problem is that the space-time used to describe a 'one way;' black hole embedded within space-time, is not the same as the configuration of space-time as the one near the Big Bang itself. Black holes have a physical 'embedding space' associated with them, while there was no pre-existing embedding space for the Big Bang!