The phrase you refernce, "a light to the nations" comes from Isaiah 51:4. Here it is in context:
You will notice that it isn't about Israel making all nations better. In fact, the text itself doesn't say that it is Israel that is the light, but rather God's justice as expressed in the Law that he gave to Israel. The classical understanding of this text then is that Israel is supposed to live in such a way that she becomes like a lighthouse, a beacon that show the way for others to live in proper relationship with God.Isaiah 51
1 "Listen to me, you who pursue righteousness
and who seek the LORD :
Look to the rock from which you were cut
and to the quarry from which you were hewn;
2 look to Abraham, your father,
and to Sarah, who gave you birth.
When I called him he was but one,
and I blessed him and made him many.
3 The LORD will surely comfort Zion
and will look with compassion on all her ruins;
he will make her deserts like Eden,
her wastelands like the garden of the LORD.
Joy and gladness will be found in her,
thanksgiving and the sound of singing.
4 "Listen to me, my people;
hear me, my nation:
The law will go out from me;
my justice will become a light to the nations.
5 My righteousness draws near speedily,
my salvation is on the way,
and my arm will bring justice to the nations.
The islands will look to me
and wait in hope for my arm.
6 Lift up your eyes to the heavens,
look at the earth beneath;
the heavens will vanish like smoke,
the earth will wear out like a garment
and its inhabitants die like flies.
But my salvation will last forever,
my righteousness will never fail.
7 "Hear me, you who know what is right,
you people who have my law in your hearts:
Do not fear the reproach of men
or be terrified by their insults.
8 For the moth will eat them up like a garment;
the worm will devour them like wool.
But my righteousness will last forever,
my salvation through all generations."
9 Awake, awake! Clothe yourself with strength,
O arm of the LORD;
awake, as in days gone by,
as in generations of old.
Was it not you who cut Rahab to pieces,
who pierced that monster through?
10 Was it not you who dried up the sea,
the waters of the great deep,
who made a road in the depths of the sea
so that the redeemed might cross over?
11 The ransomed of the LORD will return.
They will enter Zion with singing;
everlasting joy will crown their heads.
Gladness and joy will overtake them,
and sorrow and sighing will flee away.
12 "I, even I, am he who comforts you.
Who are you that you fear mortal men,
the sons of men, who are but grass,
13 that you forget the LORD your Maker,
who stretched out the heavens
and laid the foundations of the earth,
that you live in constant terror every day
because of the wrath of the oppressor,
who is bent on destruction?
For where is the wrath of the oppressor?
14 The cowering prisoners will soon be set free;
they will not die in their dungeon,
nor will they lack bread.
15 For I am the LORD your God,
who churns up the sea so that its waves roar—
the LORD Almighty is his name. 16 I have put my words in your mouth
and covered you with the shadow of my hand—
I who set the heavens in place,
who laid the foundations of the earth,
and who say to Zion, 'You are my people.' "
Did she do this?
Well, now I am biased. I am not Israelite. I am not a Jew. From my persepctive, the answer is NO. Indeed, the early Christian church read parallel ideas found in Isaiah 60
During the development of rabbinic Judaism, this passage came to be interpreted by the Jews as having a Messianic character to it. That is that though the nation of Israel might not be successful at being a light, that the promised Messiah would be, and in contradistinction to Islams understanding of the Messiah's role, the Messiah of Rabbinic Judaism was seen as bringing back into the fold not just Jews, but also Gentiles. See Isaiah 49:6 --Isaiah 60
1 "Arise, shine, for your light has come,
and the glory of the LORD rises upon you.
2 See, darkness covers the earth
and thick darkness is over the peoples,
but the LORD rises upon you
and his glory appears over you.
3 Nations will come to your light,
and kings to the brightness of your dawn.
4 "Lift up your eyes and look about you:
All assemble and come to you;
your sons come from afar,
and your daughters are carried on the arm.
5 Then you will look and be radiant,
your heart will throb and swell with joy;
the wealth on the seas will be brought to you,
to you the riches of the nations will come.
6 Herds of camels will cover your land,
young camels of Midian and Ephah.
And all from Sheba will come,
bearing gold and incense
and proclaiming the praise of the LORD.
7 All Kedar's flocks will be gathered to you,
the rams of Nebaioth will serve you;
they will be accepted as offerings on my altar,
and I will adorn my glorious temple.
8 "Who are these that fly along like clouds,
like doves to their nests?
9 Surely the islands look to me;
in the lead are the ships of Tarshish,
bringing your sons from afar,
with their silver and gold,
to the honor of the LORD your God,
the Holy One of Israel,
for he has endowed you with splendor.
10 "Foreigners will rebuild your walls,
and their kings will serve you.
Though in anger I struck you,
in favor I will show you compassion.
11 Your gates will always stand open,
they will never be shut, day or night,
so that men may bring you the wealth of the nations—
their kings led in triumphal procession.
12 For the nation or kingdom that will not serve you will perish;
it will be utterly ruined.
13 "The glory of Lebanon will come to you,
the pine, the fir and the cypress together,
to adorn the place of my sanctuary;
and I will glorify the place of my feet.
14 The sons of your oppressors will come bowing before you;
all who despise you will bow down at your feet
and will call you the City of the LORD,
Zion of the Holy One of Israel.
15 "Although you have been forsaken and hated,
with no one traveling through,
I will make you the everlasting pride
and the joy of all generations.
16 You will drink the milk of nations
and be nursed at royal breasts.
Then you will know that I, the LORD, am your Savior,
your Redeemer, the Mighty One of Jacob.
17 Instead of bronze I will bring you gold,
and silver in place of iron.
Instead of wood I will bring you bronze,
and iron in place of stones.
I will make peace your governor
and righteousness your ruler.
18 No longer will violence be heard in your land,
nor ruin or destruction within your borders,
but you will call your walls Salvation
and your gates Praise.
19 The sun will no more be your light by day,
nor will the brightness of the moon shine on you,
for the LORD will be your everlasting light,
and your God will be your glory.
20 Your sun will never set again,
and your moon will wane no more;
the LORD will be your everlasting light,
and your days of sorrow will end.
21 Then will all your people be righteous
and they will possess the land forever.
They are the shoot I have planted,
the work of my hands,
for the display of my splendor. 22 The least of you will become a thousand,
the smallest a mighty nation.
I am the LORD;
in its time I will do this swiftly."
"It is too small a thing for you to be my servantIt is this understanding that led the early church to speak then of Jesus, who they understood to be the Messiah, as the "Light of the World" and to expand the very Jewish cult that was the proto-church to within the first generation include Gentiles as well.
to restore the tribes of Jacob
and bring back those of Israel I have kept.
I will also make you a light for the Gentiles,
that you may bring my salvation to the ends of the earth."
So, you can see that the concept of what it means to be a light can vary from one person or group of people to another. The standard that you use is not that which groups before you understood was meant by the term. They may have failed to be the light to the nations that they were called to be, but not for the reasons you cite. For modern Jew, there remains the belief that they are yet called to be a light to the nations. But their perspective on what that means differs significantly from yours:
Our purpose is to promote and teach the eternal Biblical values of Israel and to build a bridge of understanding between Jews and Gentiles, based on shared values and beliefs, common roots of faith, and the realization of the hand of G-d upon us all during these special days... the days of the beginning of the Ultimate Redemption, when we sense the prophetic fulfillment leading up to the arrival of the messiah and the complete Restoration - of Israel, of man’s faith, and ultimately, of G-d’s Honor and Kingdom.
(source: Light to the Nations)
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