My family is Jewish, and last year during Hannukah I learned something about this that makes some of the information posted here, while accurate at one time, partially dated due to an event that occurred last December in Jewry.
In response to changes in the Roman Catholic Church towards Jews and Israel, Orthodox rabbis from around the world have come to the agreement that Christianity is part of God's redemption for the world. (See http://cjcuc.com/site/2015/12/03/orthodox-rabbinic-statement-on-christianity/ for more details.)
Prior to this statement the other branches of Judaism have had an accepting but nonetheless standoffish view of Christianity. However, this latest declaration refers to Christianity as 'no accident,' and recognizes Jesus, for the first time, as a Jewish "sage." The statement calls Christianity and the work of Jesus part of God's providential plan, and Judaism's current partnership with the Roman Catholic Church a genuine expression of "tikkun olam," God's work of redemption in the world.
While it recognizes that this in no way makes the two religious traditions compatible in theology and doctrine, it does state that this is not necessary for this partnership. It recognizes Jesus in the way great rabbis in the past have who saw Jesus as God's instrument to turn the Gentiles away from idol gods.
What does this mean as to how Jesus is to be viewed by the Jews and the reasons given up to this point for his rejection as Messiah? Don't expect a sudden conversion, but there has already been a lot of Jewish rabbis and instructors admitting that pride and stubbornness has played a part in keeping outdated prejudices about Jesus and Christians alive in the Jewish world.
A couple of years ago Jews released their first commentary and study version of the New Testament, "The Jewish Anotated New Tetsament: NRSV." It has also become a recent custom of some Jews to read 1 and 2 Maccabees during Hannukkah from Catholic translations such as the NABRE since Catholics preserved these texts while Jewry did not (even though these are the books that tell the Hannukkah story). This is part of a growing movement within Jewry to reclaim the Deuterocanonicals and the New Testament as products of the Jewish culture and to yield from them a better understanding of Hebrew culture and history.
So some of the arguments you may read above are still valid, but some have to be read with an asterisk taking the current flux into consideration. Again this is not saying all the Jews are happily embracing Jesus (the above statement includes the Catholic Church's current stand against any type of proselytizing of the Jews and destruction of their culture), but it is no longer denunciating the position taken by Gentile worshippers of the God of Abraham.
And the document does say that Jews and Christians don't have to debate this issue or convert one another to their views as it is part of God's purpose to have these two seemingly opposites work in unison for the same divine purpose. The Church in kind has responded by stating the Jewish covenant with God is still valid and irrevocable, and that attempts to convert the Jews to Christianity is apparently not part of the economy of providence.