Chances are that you grew up in a two-parent family, a mom and a dad. Went to a local school, away to college, married, had children of your own. And then, tragedy struck and your mother passed away, leaving your father a widower. He has mourned his loss and, in time, while still embracing the memories of your mother, met someone new and fallen in love, ready once again to enjoy a full life, perhaps to even re-marry, and you find yourself exchanging parenting roles as you concerns are not unlike that of your parents when you dated, fell in love and eventually married. While their expectation is that you will be thrilled when your older parent finds happiness in remarriage or has someone special in his life, it is seldom that simple.
It could be that you have been protective of your parent, especially caring since he became a widower and are uncomfortable with someone else taking over your role. Or perhaps this new person is assuming the role of your much-loved deceased parent. You may perceive the new partner as competition for your parent