Why do Beatrice and Benedict talk about loving each other only according to "reason"? How do they really feel about each other?

Beatrice describes Benedick thusly:

for it is all the wealth that he hath left,
to be known a reasonable creature. Who is his
companion now? He hath every month a new sworn brother.

Later, they jest:

BENEDICK

Do not you love me?

BEATRICE

Why, no; no more than reason.

Reason is a thread throughout the play; several characters use the word or its variation: John, Claudio, Dogberry, Antonio.  With everyone using it, it must have so many meanings that it becomes an empty word.  Alas, so too it is with "love."

In the Aristotlean rhetorical triangle, "reason," or ("logos"), is the opposite of "love," or ("pathos").  So, Shakespeare begs the question: do we love with our heads or our hearts?

Enter two lovers who love too wisely: Beatrice and Benedick.  They clearly love with their heads, unlike Claudio and Hero who love with their hearts.  Benedick and Beatrice give many "reasons" why they will never marry, as if they are trying to talk themselves into thinking thusly.  We know, as do the others on stage, that they don't really mean it.  Remember what Benedick says at the end?

BENEDICK

A miracle! here's our own hands against our hearts.
Come, I will have thee; but, by this light, I take
thee for pity.

In other words, here's our reason against our emotion.  So, what reasons does he give for loving her?  He writes her a poem, an emotional response.  Poetry is emotion filtered by reason.  It is a combination of emotionally-charged words put in the perfect order by reason.

How do we love? Shakespeare's answer is: "our heads against our hearts."

Claudio and Hero rush into love.  It's love at first sight, like Romeo and Juliet.  Benedick and Beatrice are more like Mercutio; they have the rapier wit that seems the very antithesis of emotion.  It is this very reason that so stabs their hearts into submission.