Peter reminds his readers that their “Life Together” came from the Word of God. That word came in baptism (“you have been born again”) and in preaching (“this is the word that was preached to you”). By obeying the preached word, a working of the Spirit, they were purified (“you have purified yourselves by obeying the truth”).
That true and eternal word produces love for one another in our ever-changing lives (quoting Isaiah 40:6-8).