That's what I'd call hijacking the conversation:
Take over (something) and use it for a different purpose:
the organization had been hijacked by extremists
MORE EXAMPLE SENTENCES
The public power belongs to everyone and when majorities hijack it for sectarian purposes they act oppressively.
Where Pringle is even-handed in showing how extremists have hijacked the debate over GM food, Nestle is an unapologetic partisan.
We should not let racist organisations hijack our national flag.
(Definition and examples from Oxforddictionaries.com)
Sometimes, a person who hijacks the conversation could be termed an attention whore:
Label given to any person who craves attention to such an extent that they will do anything to receive it. The type of attention (negative or positive) does not matter.
(Definition from Urbandictionary.com)