I've seen this discussed here a bit and there is a lot of misinformation so here are some of the key (but not all) reasons Jews do not believe in Jesus.
The Messiah must be from David's line and from the tribe of Judah, Jesus was not.
The Messiah must rebuild the temple, the temple still stood when Jesus lived.
The Messiah must reunite the Jews, the Jews were not even scattered when Jesus lived.
The Messiah must be Jewish... duh.
The Messiah will establish world peace and rule justly, Jesus did not do this.
The Messiah will rule when the Torah is written in everyone's heart and all people acknowledge Hashem as G-d, Jesus did not do this.
In addition Jews do not accept the notion of a trinity or original sin. We do not believe G-d will assume a human form. Nowhere in Messianic prophecy is the Messiah G-d in human form or otherwise. Jews also do not believe anyone can assume responsibility for the sins of another. G-d also calls human sacrifice an abomination and condemns it in the strongest possible terms. There is nothing in Messianic prophecy about the Messiah dying and coming back at a later date, it says he will finish the job.
There's more, but that's a primer for anyone interested.
A lot of people think Jesus (a) acknowledged the Torah and Tanakh in full. I don't think this is the case. If Gospels are from God it can be read that the position of Jesus (a) was occupied by John (a) before him as far light and exalted word of God type leadership. When disciples (two of them) see Elijah (a) and Moses (a) with Jesus (a), this it self is a big sign and awakening. One is dead (Moses (a)) but appears to them, one has came from heaven but never died (Elijah) and Jesus (a) is there. They wanted to make three lights in honor of them, three candles, because they are all light from God.
I think Gospels can be read in a way that say all the anointed kings of God (not just Jesus) are word of God, light, so this would mean for example, Solomon (a) didn't die a pagan nor deviate.
It's not simply working with the paradigm of Torah to Tanakh all correct. That was something Church decided to believe in and form the Bible, but it has no basis in the Gospels nor words of Paul.
Paul explanation of Lot being righteous and the exalted leader who handed the position of leadership and who has inherited by Abraham in that respect, shows, that Paul does NOT ACKNOWLEDGE ALL OF TORAH AND TANAKH TO BE CORRECT.
Paul relates the sword of God position of Jesus (a) from origins with Adam (a) all the way to now. It's very clear, one leader after another. Holy spirit always on earth.
Moses (a) Elyas (a) and Jesus (a) are EQUALS. This is the truth of the TWELVE LION STATUES with Solomon (a). They are his predecessors and his successors which are all lions of God.
The word for tribe in Hebrew can be translated as branch in many places, and the twelve branches of the children of Israel were not necessarily and probably never ever referring to actual tribes. It probably was referring to the twelve branches of Moses (a) starting from Aaron (a) down to Jesus (a) as the twelve.
The twelve gates in heaven are not going to split according to blood lineage of a tribe. Sorry that makes no sense.
The Quran corrects both Judaism and Christianity in that it shows the religion of God precedes these religions while these two religions rely on particularity. Jesus (a) centralized - if so what was the religion before him? Jews entrusted as a chosen representative of God, what about nations before? Why none of them chosen?
Seems it's not consistent.
Also Quran grounds the words of Jesus (a) and Shiite hadiths also show similar words spoken by Imams (a) about leadership, themselves, and Welayat. See the thread about Gospels and Shiite hadiths match up.