It's basically for the same reason they don't follow many of the Levitical laws such as keeping kosher, not mixing fabrics, and not worrying about ritual purity.

The main reason Christians do not participate in these things is because they view the Old Testament (the Hebrew Bible) as a precursor, pointing the way to Jesus Christ as the fulfillment of the Old Testament's prophecies. The Old Testament had a system for atonement (paying the price for sins), which included sacrificing animals (the wages of sin is death). For Christians, Jesus' death on the Cross was the ultimate sacrifice, atoning at once for all sin everywhere. No longer any need to strictly follow all the minutiae of the Old Testament and the Talmud about sacrificing sheep, cows, goats, and birds. Jesus took care of that.

In addition, in Acts 10, God gave the Apostle Peter permission to eat unclean animals (basically, permission to no longer follow ancient purity laws, including keeping kosher, mixing fabrics, ritually bathing in a mikveh, etc). In the words of the Apostle Paul, "all things are permissible, but not all things are beneficial" (1 Corinthians 10). This basically means that rather than having a huge list of things to do or not to do (the Law of the Old Testament), instead in the New Covenant of the New Testament, one is supposed to model one's life on that of Jesus, and strive to live like Him rather than obey a set of boundaries.

Most of the Jewish holidays revolve around some sort of sacrifice. Yom Kippur, for example, is the Day of Atonement, when according to the Old Testament, you were supposed to sacrifice an animal to pay for the sins you have committed in the last year (remember the wages of sin is death). This holiday is thus no longer necessary to the Christian because of Jesus' atoning sacrifice for all our sins, and the sacrifice no longer needs to be repeated. Instead, the Christians celebrate Easter, the weekend when Jesus' sacrifice atoned for our sins.

Generally, since the old Law is no longer considered to be binding to Christians, and is instead treated as a pointer for what God considers to be good (again remember that Christians are focused on living a life based on Jesus' example rather than a life focused on keeping to a strict set of rules), many of the requirements, punishments, sacrifices, and festivals outlined in the Old Testament are no longer followed because they have fulfilled their purpose, and Jesus has fulfilled them with His sacrifice.

That being said, there is nothing wrong about Christians celebrating Jewish holidays. I have celebrated Hanukkah and Passover several times (not every year like the Jews do, but occasionally). In fact, Jesus celebrated the festivals himself, so there is no reason that modern Christians should not do so as well. It is merely that Christians feel it is no longer necessary for our salvation to celebrate them.