Characters
I had rather hear my dog bark at a crow than a man swear he loves me.
— Beatrice

Behind the line May contain spoilers.
Our reading
An editorial interpretation.
The speaker ranks a dog barking at a crow above hearing a man's declaration of love. The deliberately unromantic comparison turns rejection into a joke. Rather than welcoming an elaborate promise, the speaker treats even a noisy animal exchange as the more appealing thing to hear.
Context reviewed