[Theofilus]

First of all, they are not Hebrew or Jewish holidays. They are God's holidays.

The LORD said to Moses, "Speak to the Israelites and say to them: 'These are my appointed feasts, the appointed feasts of the LORD, which you are to proclaim as sacred assemblies... These are the LORD's appointed feasts, the sacred assemblies you are to proclaim at their appointed times (Lev. 23:1-2, 4)

These are not days that the Jews thought would be a good time to celebrate. These are days God told us to keep. In my opinion, that in itself is a pretty good reason to keep the feasts.

Another reason is because of what we can learn from them. One of the primary reasons God gives us for keeping the feasts is to teach our children. We don't have to have children though. We can learn from the feasts as adults also. All of the feasts have some prophetic significance. For example, Passover froshadows Christs death on the cross. Practically everything about Passover - the Passover lamb, the unleavened bread, the bitter herbs and much more - has some prophetic or symbolic significance. Those who understood those symolisms were able to understand the significance of what Jesus did. All the other festivals also have some symbolic or prophetic significance. By understanding the symbols and prophecies, we will be able to better understand those things Jesus has yet fullfill.

Another reason is that Jesus kept the feasts. He is our example, and we should try to follow his example. He kept the feasts, so If we want to be like Him, we should also keep the feasts.

And then there is also the fact that the New Testament tells us to keep the feasts.

Therefore let us keep the Festival, not with the old yeast, the yeast of malice and wickedness, but with bread without yeast, the bread of sincerity and truth. (I Cor. 5:8)

Here Paul tells the (primarily) Gentile believers in Corinth to keep the feast of unleavened bread and, by extention, Passover and the other feasts. But we are not to keep them as "Jewish holidays" to remember something God did for them back in Egypt. Now that Christ has come, the festivals take on a whole new meaning and we can keep them in their full meaning.