Why are the saints persecuted by the Antichrist?
Scripture teaches that the Antichrist persecutes the saints because they refuse to worship him or receive his mark, and because God allows this season of trial to test, purge, and purify His people before the end.
The Bible shows that when the Antichrist rises to power, he is given authority to make war with the saints and overcome them, because the saints will not bow down and worship him or take his mark. Revelation makes it plain that all who dwell on the earth will worship the beast except those whose names are written in the book of life of the Lamb; it is precisely because the saints hold to their faith in Christ and refuse this false worship that they become targets of his wrath.
This persecution is described as a time of testing, purging and proving of the people of God. The Lord allows the Antichrist to afflict and kill the saints so that He may know whether they will wait upon Him and remain steadfast in His word. Daniel says plainly that some of those who understand will fall by the sword, by flame, by captivity and by spoil, and that this happens "to try them, and to purge, and to make them white, even to the time of the end." So the suffering is not without purpose; it refines and proves genuine faith.
At the same time, this persecution is meant to display the patience and faith of the saints before a watching world. Because the church is not hidden away but fully exposed during this period, believers become the only light in the world, and their endurance under affliction gives testimony so that others who are seeking salvation may see and be drawn to the Kingdom of God. Their steadfastness even unto death becomes their testimony against the forces arrayed against them.
Finally, the persecuted saints are also assured that their suffering will be avenged. Those slain for the word of God and their testimony are told to rest a little season until the full number of their brethren who are to be killed as they were is completed, showing that the Antichrist's persecution has a set limit and that God will ultimately judge those who shed the blood of His people.
The scriptures
And it was given unto him to make war with the saints, and to overcome them: and power was given him over all kindreds, and tongues, and nations. And all that dwell upon the earth shall worship him, whose names are not written in the book of life of the Lamb slain from the foundation of the world. If any man have an ear, let him hear. He that leadeth into captivity shall go into captivity: he that killeth with the sword must be killed with the sword. Here is the patience and the faith of the saints.
And when he had opened the fifth seal, I saw under the altar the souls of them that were slain for the word of God, and for the testimony which they held: And they cried with a loud voice, saying, How long, O Lord, holy and true, dost thou not judge and avenge our blood on them that dwell on the earth? And white robes were given unto every one of them; and it was said unto them, that they should rest yet for a little season, until their fellowservants also and their brethren, that should be killed as they were, should be fulfilled.
And such as do wickedly against the covenant shall he corrupt by flatteries: but the people that do know their God shall be strong, and do exploits. And they that understand among the people shall instruct many: yet they shall fall by the sword, and by flame, by captivity, and by spoil, many days. Now when they shall fall, they shall be holpen with a little help: but many shall cleave to them with flatteries. And some of them of understanding shall fall, to try them, and to purge, and to make them white, even to the time of the end: because it is yet for a time appointed.
From the books
This answer is drawn from these passages in the Mary Banks Faith Library.