Even though the Philippians loved Jesus and Paul, they didn't love each other as they ought to. The Christmas story is supposed to have an impact on our everyday lives. It's an invitation to die to our selfish desires and be like Christ.
The problem of human sin could only be solved by having God become human to live under the Law, fulfill everything commanded, and then die on our behalf. The only reason salvation is possible is because Jesus didn't insist on keeping his glory when he was human; he became a lowly servant despite being God.
Pride is the downfall of many, however, Jesus humbled himself and shielded his divinity so people could approach without great fear and be accessible to everyone.
Paul asks the Philippians to remember how Jesus lived and died and to have the same attitude. If we should have the some mindset as Christ, then we can't help but love one another.