The answer is:
Linda: Well, we can use this word for water.
Matthew: Huh? It sounds like you don't know water is made of atoms.
Linda looks at water and sees it to be a fluid; you can count grains of sand, or rocks, or people, but you don't typically "count" water, you measure it, typically in litres.
Matthew rebuts her by saying that water is made of atoms, making the point that they could be counted.
Linda: What? What about using this word for love?
Matthew: That's even more absurd. Love cannot even be measured.
Linda: How is that more absurd when you're actually concurring by that last sentence?
Linda suggests using "uncountable" for love. It sounds strange and ill-fitting, and Matthew highlights this fact. But, Linda ripostes by explaining that his rebuttal actually proves her point.
Love literally cannot be measured, and so it is literally uncountable.
Matthew: Listen, this word is used for things that are too many!
Linda: You cannot say "many" for the things that this word is used for!
Finally, Matthew makes the point that the word ("uncountable") is in reference to an infinite number of things. That is, a quantity of things that is infinite, and so cannot be counted.
Linda, staying on form, holds to the literal view; if something is "uncountable", you can't count it. You can't say "many" because you can't count it to begin with.
Regarding the names as clues:
Matthew always takes a mathematical approach; his views reflect the academic meaning of the term; an infinite set.
Linda always takes a linguistic view. She approaches the problem in terms of the English language and phrasing, which is why she often appears to be speaking in very literal terms.