RITA: Believe it or not, I studied 19th-century French poetry.
PHIL: What a waste of time.
Phil Connors doesn't really have the wisdom to appreciate the fact that Rita loves French poetry enough to study it at university. To him, studying poetry is a total waste of time because it's not practical. It's not until later in the movie that Phil learns to respect people's differences.
PHIL: I wish we could all live in the mountains, at high altitudes.
Phil tells Rita that he wants to live a peaceful life away from the hustle and bustle. But the truth is that he's only saying this because he thinks it's what Rita wants to hear.
RITA: I like to go with the flow, see what happens.
Rita has a lot of wisdom because she has learned to accept life as it comes. This acceptance is a big part of what makes her so kind and compassionate toward others.
RITA: I can't believe I fell for this.
Rita eventually sees right through Phil's attempts to trick her into bed with him. She has the wisdom to understand when a person behaves and certain way and when they genuinely feel a certain way. That's the kind of wisdom that it takes Phil a really, really long time to develop.
PHIL: When Chekov saw the long winter, he saw a winter bleak and dark and bereft of hope.
After he's stuck in Groundhog Day for a long time, Phil decides to start developing his wisdom by reading classical works of literature. All this reading definitely has an impression on him, as he starts quoting it in his news broadcast.
PHIL: Yet we know that winter is just another step in the cycle of life.
Over time, Phil learns to think of life as a cycle rather than an endless chase to get what you want. It's this kind of wisdom that will eventually lead him to be kinder and gentler to the people around him.
PHIL: I've never seen anyone that's nicer to people than you are.
It takes a while, but Phil eventually learns to be honest with himself. The first thing he admits to himself is how deeply he admires Rita's kindness to other people.
PHIL: We never talk, Larry. Do you have kids?
Phil quickly realizes that his wisdom and knowledge doesn't count for much unless he uses it to improve the lives of the people around him. That's why he needs to apply his compassion to more people than just the woman he loves (Rita). He needs to apply it to everyone.
PHIL: I'd like a piano lesson, please.
Phil figures that if he's going to be stuck in the same day for eternity, he might as well use the opportunity to get really good at something. So he gets up one day and decides to spend the next ten years' worth of Groundhog Days playing the piano.
LARRY [to Rita]: Did you know he could ice sculpt?
Along with his piano skills, Phil decides to learn how to ice sculpt. Why not? After all, wouldn't you eventually turn to art if you had to live the same day over and over for eternity?