The Baxter Reminds Us that Meet Cutes Don't Happen in Real Life
The term "meet cute" is commonly used to refer to the first meeting between two future romantic characters that's particularly adorable. Most, if not all, romantic comedies include meet cutes that seem forced or unrealistic. The Baxter, on the other hand, purposely uses a meet cute that can only be described as ridiculous in order to remind the audience that experiencing a meet cute in real life is impossible.
As soon as the scene starts, we can already see the, well honestly, weird direction the meet cute is going in. The conversation Cecil and Eliot have about reading the dictionary is the important part here. The fact that they share the same interest in doing something that seems completely insane is the start of The Baxter's hilarious/weird meet cute.
Towards the end of the scene, they even mention how weird it is that they have found each other since they have a common interest. The film does this by giving them a back-and-forth describing the meeting with different words that -- if we are to believe the characters -- learned by constantly reading the dictionary.
By doing this, the people that made the film are subtly nudging our elbow as if to say, "aren't meet cutes, a little, you know, ridiculous"? By making their meet cute so outlandish, The Baxter reminds the audience that meeting someone in real life is nothing like it is in the movies.