Is a celibate priest allowed to be in love with a woman?

He promises to keep the relationship chaste, and he's asked for "a dispensation to go out with her." The answer is no:

The Rev. Sante Sguotti can no longer work as pastor in his Monterosso parish and cannot hear confessions from the faithful, the diocese of Padua said in a statement....

Is the main problem that they don't believe he'll remain chaste — the woman had a baby that he helped name — or that we don't want to see him openly dating a woman? Or is it that a priest is supposed to be devoted to the whole congregation and not fixated on one individual?