Why can't Col. Fitzwilliam pursue Elizabeth as a bride?

Answer 1

Neither Col. Fitzwilliam nor Elizabeth has any appreciable amount of money. As a younger son of an earl, he should be able to marry a woman with a considerable fortune, which he really needs to do because of his own lack of one. He could marry Elizabeth, if they really fell in love, but he would have to take up some kind of work for which he was not prepared, and then they would have to live with the fact that they had both sacrificed quite a lot to be together. So they each considered the other out of bounds as a partner.

Answer 2

Poor Darcy has had women after him for years. Bingley's sisters have laid claim to him, as has his aunt, and probably every other woman he meets, for herself, a relative, or even a friend. He is handsome, well bred, and rich.

In Elizabeth, he finds a pretty girl, intelligent and somewhat accomplished, who makes no effort whatever to lay claim to him, to get him to fall in love with him, or even to get to know him. Here is something different from every other woman he has ever known. It is intriguing for him and gets him to investigate. The more he learns about her, the more he realizes a match would be unsuitable, and tries not to be attracted. The more he tries not to be attracted, the deeper he falls in love.