Why not? There’s nothing that requires us to make resolutions at the start of the new year as Catholics, however, we do seem to be a religion that holds this practice in high regard.
Each time we go to confession we “firmly resolve with the help of God’s grace” not to sin again. We renew the promises we made at baptism during the Easter Vigil and at other times. We make a public display of making some kind of resolution at Lent as well.
So my advice is that while we don’t HAVE to do this at New Year’s perhaps we use this period of time as a warm-up for Lent. We should think about something that we might want to give up for Lent that is seriously unhealthy for us and begin to make a resolution plan to implement for the 40 days of Lent. This way, the pressure is off to jump right into a resolution but more importantly, we take this time to discern what we really want to change instead of superficially jumping into a resolution that really doesn’t change much in our lives.