Almásy is a man who doesn't believe in adjectives, but Katharine demonstrates that there are many different kinds of love. Almost all of these loves are present in the movie.
ALMÁSY: You can't explore from the air, Madox. If you could explore from the air, life would be very simple.
Following up the last quote, Almásy is a man who maps things from the ground, but he flies through life, not wanting to get up close and personal with it. Katharine shows him the depths of love, but he has to explore her from the ground (so to speak), to understand it.
ALMÁSY: I think you've got the wrong end of the stick, old boy.
Here is an example of platonic love. Or maybe filial love, the love of a child for a parent. Hana loves Almásy but not romantically. She either loves him as a friend, or as a stand in for her own father.
HANA: I'm not in love with him. I'm in love with ghosts. So is he. He's in love with ghosts.
Caravaggio accuses Hana of loving Almásy in a romantic sense. She clarifies that she does not. But both Almásy and Hana are haunted by romantic loves of the past. Romantic love might be the strongest—and most dangerous—love.
BERMANN: How do you explain to someone who has never been here, feelings which seem quite normal?
What is it about the desert that rewrites the rules of love? Is the desert itself, and its shifting sands? Or is it simply being so far from home? Many characters fall in love with people that they probably wouldn't love if they were back home. Almásy and Katharine. Hana and Kip. And here, Bermann, a married man, and a young man named Kamal.
ALMÁSY: What do you love?
KATHARINE What do I love? ALMÁSY: Say everything.
KATHARINE: Let's see… water. The fish in it. And hedgehogs. I love hedgehogs. ALMÁSY: And what else?
KATHARINE: Marmite. I'm addicted. And baths. But not with other people. Islands. […]
Katharine's list of what she loves are all mostly things she can't get in the desert. Does one kind of love outweigh another? Can Katharine's love for her husband, or for Almásy, outweigh her sadness at missing all these other things she loves? We don't think so. In a love battle between hedgehog and Almásy, hedgehog wins.