"She's everything. He's Just Ken."

Barbie = { Everything }

Ken ∈ Everything

∴ Barbie is Ken

Given that Barbie is everything and that Ken is a member of the set Everything, we therefore know that Barbie is Ken.

@LilahTovMoon

In Barbie’s world Ken is like a skin tag on her neck. Visible, useless, and a slight annoyance.