This is an excellent question to consider. I would actually argue that there are a number of characters in this wonderful novel who show that they are incapable of love, whatever their words actually indicate. You have identified that Tom is one of these, but I would also add Bounderby and of course Louisa to the list. In the case of Bounderby, we have a character whose life is built on a fabrication of lies and arrogance. He is incapable of understanding Louisa, his wife, and incapable of loving another human, even treating his mother in a terrible way.
For Louisa, and for Tom, we can identify that their inability to love is a direct result of having being brought up under the full influence of their father's educational philosophy. They have been brought up in a life that has only acknowledged facts and conveniently done away with fancy. Note what Louisa herself says to her father when she asks him his opinion about her marriage to Bounderby:
"What do I know, father," said Louisa in her quiet manner, "of tastes and fancies; of aspirations and affections; of all that part of my nature in which such light things might have been nourished? What escape have I had from problems that could be demonstrated, and realities that could be grasped?" As she said it, she unconsciously closed her hand, as if upon a solid object, and slowly opened it as though she were releasing dust or ash.
Louisa is incapable of love, just as Tom shows himself to be, thanks to the way that love, emotions, feeling and fancy were never part of her childhood in any way. The way that she "unconsciously" picks up and let fall an imaginary pile of ash shows the true barren nature of her life as a result. Being unable to love, being unable to connect emotionally, she remains emotionally stunted as an individual.