Othello does love Desdemona; it's possible to look at his violent, jealous love as something other than love, but ultimately, he does love her. Perhaps, though, the love he bears for her is not healthy.
Othello kills Desdemona because he sees her supposed indiscretion with Cassio as a betrayal. It isn't that he's embarrassed that she supposedly cheated on him; it's that he can't stand the idea of such a deep betrayal. As she lies there sleeping, he says:
Let me not name it to you, you chaste stars,
It is the cause. Yet I’ll not shed her blood,
Nor scar that whiter skin of hers than snow
And smooth as monumental alabaster.
Yet she must die, else she’ll betray more men.
Put out the light, and then put out the light.
He calls her the light because she is the brightness in his life. She brings him happiness and joy. However, now that she has betrayed him with another man, he can't imagine forgiving her or allowing her to continue to live. He's torn, though, because he looks at her and doesn't want to hurt her.
However, the love Othello has for Desdemona isn't healthy. It could be argued that if he loved her in a healthy way, he'd have given her the benefit of the doubt or offered her a chance to explain. But he bemoans his love for her even while she's laying there and preparing to die. So in Othello's own words, he does love Desdemona. He says:
So sweet was ne'er so fatal. I must weep,
But they are cruel tears. This sorrow’s heavenly,
It strikes where it doth love.