The phrases "I like cheese" is most precisely used to point out a comment that was relevant some time in the past but is not relevant in the current context. It evolved over time to also point out any non-sequitur comment.
This was started during a discussion between two students at Gustavus Adolphus College in St. Peter, MN. The one student (from Minnesota) called the other student (from Wisconsin) a "cheese head". The conversation continued on to other topics and the "cheese head" comment was long forgotten. Several minutes and topics later, the student from Minnesota (likely feeling the pangs of guilt for the forgotten insult) turned to the student from Wisconsin and said, "I'm sorry I called you a cheese head. I like cheese."
Dora: What do you think about the current election year?
Kris: I think that both parties have a lot to be desired.
Jenny: Speaking of parties, there is one tonight at the Kappa's house!
Becky: Cool! Maybe we can get in for free!
Scott: Let's ask Matt!