God never really wanted animal sacrifices in the first place. It was a common practice that was already taking place in many cultures (some say it originated in Egypt.) And because people were already sacrificing animals (to false gods), God enacted laws on animal sacrifice, I believe for several reasons. But it was always meant to be a temporary thing. God sometimes works with us where we're at, in order to get us to where He wants us to go.
Please read these passages. I'll bold the pertinent parts.
Psalm 40:6
Sacrifice and offering You did not desire;
My ears You have opened.
Burnt offering and sin offering You did not require.
Psalm 51:16-17
For You do not desire sacrifice, or else I would give it;
You do not delight in burnt offering.
The sacrifices of God are a broken spirit,
A broken and a contrite heart—
These, O God, You will not despise.
Proverbs 21:3
To do righteousness and justice
Is more acceptable to the Lord than sacrifice.
Jeremiah 7:22-24
For I did not speak to your fathers, or command them in the day that I brought them out of the land of Egypt, concerning burnt offerings or sacrifices. But this is what I commanded them, saying, ‘Obey My voice, and I will be your God, and you shall be My people. And walk in all the ways that I have commanded you, that it may be well with you.’ Yet they did not obey or incline their ear, but followed the counsels and the dictates of their evil hearts, and went backward and not forward.
Hosea 6:6
For I desire mercy and not sacrifice,
And the knowledge of God more than burnt offerings.
1 Samuel 15:22
But Samuel replied:
“Does the Lord delight in burnt offerings and sacrifices
as much as in obeying the Lord?
To obey is better than sacrifice,
and to heed is better than the fat of rams.
Isaiah 1:11-17
“To what purpose is the multitude of your sacrifices to Me?”
Says the Lord.
“I have had enough of burnt offerings of rams
And the fat of fed cattle.
I do not delight in the blood of bulls,
Or of lambs or goats.
“When you come to appear before Me,
Who has required this from your hand,
To trample My courts?
Bring no more futile sacrifices;
Incense is an abomination to Me.
The New Moons, the Sabbaths, and the calling of assemblies—
I cannot endure iniquity and the sacred meeting.
Your New Moons and your appointed feasts
My soul hates;
They are a trouble to Me,
I am weary of bearing them.
When you spread out your hands,
I will hide My eyes from you;
Even though you make many prayers,
I will not hear.
Your hands are full of blood.
“Wash yourselves, make yourselves clean;
Put away the evil of your doings from before My eyes.
Cease to do evil,
Learn to do good;
Seek justice,
Rebuke the oppressor;
Defend the fatherless,
Plead for the widow.
Micah 6:8
He has shown you, O man, what is good;
And what does the Lord require of you
But to do justly,
To love mercy,
And to walk humbly with your God?