God's Word nourishes us

Even if we have not been parents ourselves, we have probably known family members who have brought home newborn babes, and one thing that our Creator God instills in these wee ones is a motivation, a craving, an instinct to find mother's milk. These new lives are "programmed" if you will, to turn toward anything that brushes their cheek, as if to latch on to mom's breast and receive that nourishment. And they have a powerful response to anything that lands on or in their mouth! If you place the tip of your finger in their mouth (sure hope you washed your hands first) they will suck VERY vigorously on that.....until, of course, they realize they aren't getting anything, and then they will let loose and cry!
Peter is saying that we should be just as motivated to drink in God's Word.
How do we get that kind of motivation? That craving? That intense desire? There are so many things clamoring for our time and attention in this mortal world....
He gives us two strategies rolled into one.
Ready?
Let's look at our verses again:

Therefore, rid yourselves of all malice and all deceit, hypocrisy, envy, and slander of every kind. 2 Like newborn babies, crave pure spiritual milk, so that by it you may grow up in your salvation, 3 now that you have tasted that the Lord is good. (I Peter 2:1-3, NIV)

The first thing Peter tells us to do is to get rid of some sins that hinder the Word's effects in our lives. In the NIV, which I posted there, the words are translated "rid yourselves" but in others, we read "put off." To put off means to cast aside these sins, just as when you come in from working on the fence-line beside the driveway and your clothes are muddy. You toss them aside. (In that case, you want those clothes back again after they've been washed, but that's another story.)  Just as you toss aside dirty clothes, Peter says to put off these sins..... these are baggage from our past. Before we were saved. And they can hang on, like the mud on your boots. These surround us, after all, in this sinful world, and they are standard operating procedure for many people in this world! Especially when they get into tough situations!
But Peter notes here that they can hinder our spiritual growth, and that they must be discarded as the filthy rags that they are. (Even what we think are "good" and righteous deeds miss the mark.)

All of us have become like one who is unclean,    and all our righteous acts are like filthy rags;we all shrivel up like a leaf,    and like the wind our sins sweep us away. (Isaiah 64:6)

Let's look at Peter's list..... "malice" is a general word that was used to mean wickedness of every kind, but it especially referred to having a grudge or seeking to harm someone. "Deceit" is an easy one.... to trick or mislead someone by telling them something that isn't true. Usually means you are full of ulterior motives in your dealings with the other person. "Hyprocrisy" we've noted before comes from the word that means to wear a mask; it refers to the many ways that we can fool people by projecting a false image. For instance, if we are inconsistent in the ways that we behave at church and at work, or other areas of life, we are hypocrites.
Envy is the root of much of the deceit and hypocrisy in this world; it means that we are jealous of another person or the things that they have.  It was even the motivation behind the crucifixion of our Savior; the religious leaders of the day were envious of His popularity. And then, envy often is demonstrated by all kinds of slander. Speaking against someone. Slander is closely tied to deceit and to hypocrisy, since the slanderer will say nice things to the person's face but then disparage them behind their back -- all with the goal of making the slanderer look good in everyone else's eyes.

As believers, our communications should be the opposite of all these worldly ways. We are to speak the truth in love, and our motives are to be pure:

Instead, speaking the truth in love, we will grow to become in every respect the mature body of him who is the head, that is, Christ.Do not let any unwholesome talk come out of your mouths, but only what is helpful for building others up according to their needs, that it may benefit those who listen. (Ephesians 4:15, 29)

Peter says that we are to put off these wrong ways of relating to other people -- he is implying that we are both responsible for these sins, and that we are able with the help of the Holy Spirit, to put them aside.  It doesn't take years of therapy. We don't need to delve into our past. We simply need to make a decisive break with our past and daily ask the Spirit for His help.

The second half of the strategy to be motivated to drink in the Word is to focus on the kindness of God:

now that you have tasted that the Lord is good. (I Peter 2:3, NIV)

For Peter, it was clear that Christ is the Lord. This is actually a quote from Psalm 34:8, and it shows that Peter believed Christ to be God (or Yahweh, to the psalmist). I wonder if Psalm 34 was one of Peter's favorites.... He quotes from it again over in chapter 3 (if you'd like to skip over and read, it's the 10th through the 12th verses). And the theme of Psalm 34 is very similar to the theme of what we call the book of I Peter; his first letter to the believers has nearly the same theme as that psalm. He tells them that if they are in distress, they should seek the Lord, and He would deliver them from all of their troubles.

In verse 3, Peter is referring specifically to the Lord's kindness and grace that was shown to us when we trusted Him as our Savior, and gave lordship of our lives to Him. If we are saved, we have tasted of the Lord's kindness, because we know very well that we deserved His judgement. Yet He showed us mercy!

But God commendeth his love toward us, in that, while we were yet sinners, Christ died for us. (Romans 5:8, KJV)

The cross of Christ, where a holy God made a provision for us, the sinners, so that we could experience His forgiveness and receive eternal life as a free gift, should be the focus of every believer, every day.

Putting off the sins of the past, and tasting of the Lord's goodness are how we remain motivated to drink in His Word, and study it every day..... we'll be growing in Him when we do!