The way I understand it (and I double-checked in some dictionaries), the term 'extinction' is used when talking about a group of beings (a species, for instance) that is dying and may stop existing. Bitcoin isn't alive, and Bitcoin isn't a type, species or anything like that, so it cannot go extinct by definition.
If you are referring to Bitcoin no longer being around, I suppose it can happen if the Internet collapses and human civilization experiences a major technological downfall. Or, alternatively, Bitcoin can potentially be rendered useless (although probably not non-existent) by technological advances in something like quantum computing.
However, if we're talking about the foreseeable future, I agree with others who say that it's highly unlikely that Bitcoin will stop existing.