To address the issue of why Judaism doesn't accept Jesus/Yeshua as the Messiah, we have to explain what the Tanach has to say about the Messiah. This is especially difficult to do since the Tanach doesn't really discuss the Messiah very much. The Hebrew word "Mashiach (Messiah)" literally means "anointed", and it appears in one form or another only a few times in the Tanach. Most of the times it appears, it refers to the objects in the Tabernacle/Temple being anointed, so it's safe to assume that those times aren't speaking about "The Messiah". Other times when the word is mentioned, it refers to a Kohen (like in Exodus 29:7), a Jewish king (like in 1 Samuel 10, or 1 Samuel 16), or a prophet (like in 1 Samuel 19:16). There's also one mention of the non-Jewish king Cyrus being referred to as Mashiach (Isaiah 45:1), it's also safe to say this probably isn't referring to "The Messiah". The closest time that "The Messiah" is spoken about using the word "Mashiach" would be when Scripture talks about a Jewish king being anointed, but even then it never refers to the Mashiach as "Mashiach", which might surprise you. So how can we understand a passage as being about "The Messiah"? As it turns out, the way both Christians and Jews determine if a passage is about the Messiah is by looking at the description of the state of the world in the passage and asking if this is the world we currently live in.
Let me give you some examples. Isaiah 11:12 speaks about a world where all of the Jewish people are brought out of Exile and returned to the Land of Israel. This hasn't happened yet, as I have no doubt that you're aware. But just to drive this point further, if you're Jewish like many in the United States are, and you don't live in the Land of Israel (which most likely applies to you like it applies to most Jews), then it's safe to say that the Messiah hasn't come to gather the Exiles back to the Land of Israel. Ezekiel 37:26-27 tells us that the Messiah will rebuild the Temple in Jerusalem. This hasn't happened yet, so we can safely say that the Messiah hasn't come yet. Micah 4:3 tells us that the Messiah will rule at a time when there is actually complete global peace, which has literally never happened in history. The existence of ISIS is all the proof we need to say that the world is not at peace, and therefore, the Messiah hasn't come yet. Ezekiel 37:24 tells us that the Messiah will rule at a time when every single Jew will keep the Torah fully. We live in a world where the majority of Jews don't even try to keep the Torah, so it's safe to say the Messiah hasn't come yet. Isaiah 66:23 tells us that the Messiah will rule at a time when every non-Jew will worship the G-d of Israel. The existence of religions like Hinduism, which has over 3 million gods, is proof enough that we aren't living in a time where every non-Jew worships the G-d of Israel, so it's safe to say the Messiah hasn't come yet. All of these Messianic qualifications are actually found in one passage, Ezekiel 37:24-28. For the record, all Jewish and Christian leaders agree that these are all Messianic prophecies and that none of them have been fulfilled yet.
We have additional information about the Messiah. For example, Deuteronomy 17:15 tells us that the Messiah must be Jewish in order to be the king of the Jews. This rules out people like David Koresh, not that you'd ever suspect him to be the Messiah. Genesis 49:10 tells us that the Messiah can't be any Jew, he must be from the tribe of Judah. We know from Numbers 1:2 and Ezra 10:3 that a Jew inherits his tribe from his father, and that a tribe is not inherited from a mother. We also know from Ezra 10:3 that a Jew inherits his Jewish identity from his Jewish mother, and not his father, which is why the children of foreign women were sent away with their mothers. 2 Samuel 7:12-13 tells us that the Messiah can't be any Jew from the tribe of Judah, he has to be patrilineally descended from King David.
So let's apply what the Tanach tells us about the Messiah and see if Jesus/Yeshua fits the Biblical criteria of the Messiah. Was Jesus/Yeshua the son of a Jewish mother? The gospel of Matthew tells us that Jesus/Yeshua was the son of Mary, but doesn't tell us if she was Jewish. But since we have no evidence to say that she wasn't Jewish, let's assume she was, which makes Jesus/Yeshua a Jew. Was Jesus/Yeshua from the tribe of Judah? Matthew 1:18 tells us that Mary was impregnated by the Holy Ghost, which means that he didn't have a Jewish father. So according to the Scripture, Jesus/Yeshua wasn't a part of a Jewish tribe, so he wasn't from the tribe of Judah. Was Jesus/Yeshua descended from King David through his father? The Holy Ghost isn't a man, so no, he was not from the patrilineal line of King David. Did Jesus/Yeshua bring the Exiled Jews back to the Land of Israel? Not only did he not return the Exiles, but the Romans exiled all Jews from Judea after the Bar Kochvah Revolt in 136 CE, about 100 years after Jesus/Yeshua is traditionally said to have been murdered by the Romans. Additionally, all the Jews left Jerusalem after the destruction of the Second Temple in 70 CE, about 40 years after the Roman murder of Jesus/Yeshua. Did Jesus/Yeshua rebuild the Temple in Jerusalem? Not only did he not rebuild the Temple, but the Second Temple was still standing when the Romans murdered him. Did Jesus/Yeshua rule at a time of global peace? Not only did he not even rule, but there have been more wars fought in his name since his murder than any other reason. Did he rule at a time when all Jews kept the Torah, or even help make any non-observant Jews Torah observant? Again, he never ruled, but not all Jews in his day were Torah observant, and there isn't enough evidence to say definitively that he helped any Jew become more observant. Did he rule at a time when all non-Jews worshipped the G-d of Israel, or at least help any non-Jews to come to worship the G-d of Israel? Again, he never ruled, there were many non-Jews who worshipped the gods in his day, and there is not enough evidence to say definitively that he helped any non-Jews come to worship the G-d of Israel. In fact, while the gospels never say that he claimed to be the G-d of Israel, about a third of the world population worships him as a god, and most of them aren't Jewish but some are. Most religions seem to try to claim him as one of theirs, which I'll admit seems like a bad attempt to say that they believe he was important to them too. Unique among religions, Judaism doesn't claim Jesus/Yeshua as anything other than a man, a Jewish man, but a man nonetheless.
So, of the major messianic prophecies that all Christian and Jewish leaders agree are Messianic, Jesus/Yeshua fits exactly zero of them. By the admission of the New Testament and every Christian alive today, he doesn't have a human father, which means the Torah says that he isn't a part of any Jewish tribe, so he's not from Judah and isn't descended on his father's side from King David. Plain and simple, Jesus/Yeshua didn't fulfil the qualifications to be the Messiah. So why are the Jewish people still waiting for the Messiah? Simply put, the Tanach says that the real Messiah hasn't come yet, so we will keep waiting until he does come.