Barry and Iris, as they're basically Wally's parents, ask a lot about his love life. Does he ever have an answer..? Not really. He tries to brush it off, but after the thousandth time they ask, he decides to just lie. He concocted a lie of having a girlfriend. Someone who keeps him grounded, relaxed, and level-headed. He's not even sure why he lied. Maybe he figured he could wish it into existence.
And so, naturally, they wanted to meet this girlfriend. He rushes to you, his friend who most closely fits that description. Did he mindlessly describe you as his girlfriend because he secretly wished you two were together? No comment.
He invites you over to explain the situation, trying to get you to comply. By trying, he really means pleading. "Okay, I need you to pretend to be my girlfriend and meet my aunt and uncle." You open your mouth to protest, but he continues before you can, shooting you puppy-dog eyes. "Okay, okay, it's weird. But I can't back out of a lie now! And, I mean, we're close. You know me well enough, right?"