The equality of all mankind is not a Jewish idea. It is a Greek/Roman/Western-democratic idea that Jews have assimilated over time. Humanity does not all exist on one level. Let's look at how Rabbi Moshe Chaim Luzzatto, ztz"l explains it with commentary provided by Torah.org's Rabbi Yaakov Feldman...
PART 1, PART 2
Derech Hashem, Part II, Chapter 4 - Israel and the Nations, Paragraphs 4 and 5
 God's great love and goodness decreed that the branches of other nations still be given a chance. If they so desired, they still had the free choice to tear themselves loose from their own roots, and through their own actions include themselves among the branches of Avraham's family.
This is what God meant when He told Avraham (Breishis 12:3), "All the families of the earth will be blessed through you." Avraham was thus made the father of all converts.
[This, however, would require effort on the part of the individuals concerned.] Without such effort, they would remain attached to their own roots and retain their natural characteristics.
 It is also necessary to realize that each individual tree is also divided, very much as the descendants of Adam were divided into Root, Trees, and Branches. Primary branches can thus be distinguished in each individual tree, and these branches are then differentiated to yield their particular members.
Avraham's tree consisted of 600,000 main branches. These were the individuals who left Egypt, and it was to them that the Torah was given and the land of Israel divided. Every Jew subsequently born is considered to be an element and descendant of one of these primary branches.
It was to these 600,000 original Jews that the Torah was given. When this occurred, the tree was said to have attained maturity.
At this time, God also gave the nations a last chance. In His mercy He had suspended their final judgment until the time that the Torah was given [with the revelation at Sinai]. He then offered the Torah to every nation, giving them the opportunity to accept it.
If any nation would have then accepted the Torah, it would have elevated itself from its lower state. As it was, none of them desired the Torah, and their judgment was therefore sealed completely. The gate was permanently closed, never again to be opened.
It still remained possible, however, for any individual to convert to Judaism. In this manner, he could still include himself in Avraham's tree of his own free will.
Torah.org - Rabbi Yaakov Feldman
Though humankind has been clustered into various root groups for many generations now, as we said, we learn here that anyone can still and all change his or her root group. Thus anyone can become an "instant descendant" of Abraham (and a Jew) at will.
We see then that becoming a Jew comes down to leaving one's original people and root group, and attaching onto the Jewish people. Hence it doesn't involve merely vowing to do this and that rather than that and this. It comes down to an utter transformation and transference from one self with one background to a wholly other self with another background. It's more than merely changing one's religion; it's changing one's very family.
Like any family, the family of Jewish-kind has its own ways, perspectives, values, and inclinations. But rather than being a series of phenomena molded by climate and circumstance, Jewish ways, values, and the like are rooted in Abraham's dreams for and directives to his family. And those dreams and perspectives were themselves rooted in one thing alone: drawing close to G-d. That all touches upon the mitzvah system. As a consequence, anyone who'd want to become a member of the "family" would have to find his or her place in the "family system" -- in the mitzvah system.
Now, there was a point in time when other nations were offered the mitzvah system as a lifestyle, but they refused. It was when Abraham's by-then 600,000 descendants became a nation unto itself, left Egypt in the great rush and whirlwind known as The Exodus, experienced the revelation of G-d Himself when He granted us His holy Torah, and attained a high level of spiritual and national maturity that could be likened to an offshoot truly and finally blossoming.
Had those other nations accepted the Torah as Abraham's descendants had, they'd also have ascended spiritually. But they decided not to. So the gate through which they too could have passed to be "chosen" was closed off to them as a whole, though it was left open to those among them who'd join Abraham's descendants.