Readings & Meanings:
connect, in charge
He seems to be connected to that affair.
I am having sexual relations with the supervisor.
I became the Class Pet Raiser.
It's not 糸.
人 is the radical here, as you can see on the left.
But on the right is not 糸.
The phonetic element is 系, which is 糸 with an extension, 丿.
So 係 is a person connecting objects with a thread. I guess only people in charge should do that.
But not with 糸.
In Japanese, there is a very useful phrase: それは関係がない。 It means, "There's no connection!" It's useful in debating things with your friends, or arguments in general (just shout 関係ない！), but it's also used when watching TV and something totally silly and absurd takes place.
Speaking of silly and absurd, below is comedian Yoshio Kojima's attempt at teaching English.
In 2007, Yoshio Kojima became famous for dancing in his underwear, pumping his fist at the ground, and saying "そんあの関係ネー！"