These are some of the most common arguments they make, and why they are invalid.
"Historians almost unanimously agree that Jesus was a real person."
No, they don't. Some strongly argue for it, others against it. Most are open to the possibility of a person named "Yeshua" having existed, who was the basis of the texts, but they don't assert it. Others propose that the "Jesus" of the text is actually an amalgamation of several people (plus a good deal of embellishment.)
The vast majority of historians would agree that it's possible that the story of Jesus is loosely based on a real person, but that the vast majority of the details about him in the New Testament are inaccurate. They also would agree that it's possible that no such person existed at all. Thus, there is no unanimous agreement.
"Most historians agree that the New Testament is historically realiable."
No, they most definitely don't. This is just an outright lie perpetuated by dishonest apologists.
In fact, there are even many Christian historians and theologians who admit to the possibility that many of the events described in the New Testament probably never happened. (Of course the apologists who perpetuate the lie will just resort to the no-true-scotsman fallacy at this point.)
"There are numerous extrabiblical sources for the existence of Jesus."
Actually, there aren't. None at all. This is another lie perpetuated by these dishonest apologists.
They will cite several historians of the first and second centuries, but in every single case these historians are not accounting contemporary historical events, but instead are describing Christians and their beliefs. Invariably, all these mentions were written many decades (sometimes even over a century) after the alleged events of the New Testament. A document mentioning Jesus is not a very reliable source if said document was written a hundred years after Jesus (allegedly) died, and in context is just describing what Christians believed.
For example, apologists just love to mention Josephus, as he mentions Jesus' followers in his text. What they don't mention is that Josephus was born in 37 AD, long after Jesus' alleged death. Hardly a contemporary eyewitness. (All the other historians that apologists love to cite were born later than Josephus, so they aren't any better.)
"The New Testament is reliable because of the thousands of eyewitnesses."
This is a perfect example of a circular argument. It argues that there were thousands and thousands of eyewitnesses to the events described in the gospels, and thus the New Testament is very reliable. But how do we know there were thousands of eyewitnesses? Because the New Testament says so. There is no other source for these alleged eyewitnesses.
I don't think it's necessary to add anything to that. It's a circular argument in its purest form. (And this isn't even going into the fact of how unreliable eyewitness testimony is, no matter how many witnesses there are.)
"The gospels cannot be inaccurate because the people who lived in those places and witnessed those events would have objected to the inaccuracies."
This is one of the favorite arguments of many apologists, and it's one of the stupidest.
Firstly, the gospels were just some books written by some people, which were copied and spread very slowly. They did not mass-print them for the masses because there was no printing technology. And even if a copy did end up in the hands of someone who had lived at one of those places at the correct time, and even if this person had realized that the described events never actually happened, so what? This person probably didn't know who had written the text, nor had the means to do something about it even if he or she wanted.
Also, even if it did happen, the person could have just thought that he didn't witness it because he was just unlucky. It probably happened on the other side of the city, or when he was not around to see it.
Secondly, the gospels were written several decades after the alleged events. Most of the potential eyewitnesses had died or were too young to remember.
Thirdly, we have actual examples of fictional biographies, or biographies with inaccuracies in them, having been written very soon after a person has died, and with nobody objecting to them or correcting them. (The biography of George Washington is a perfect example.) And these are not biographies written decades after the person's death, but almost immediately.
"The gospels cannot be a case of real history having become legendary because they were written too soon after the events."
This is appealing to the notion that historical writing cannot become distorted by legends if it's written too soon after the events. This is a misunderstanding of the original proposition, and is very demonstrably false.
It also has the big problem that it assumes that there were events to be distorted by legends in the first place. There's absolutely nothing that would have stopped the authors of the gospels from just inventing the events.
You could just as well argue that the Harry Potter books were written too soon after the events they describe in order for them to be inaccurate. It makes absolutely no sense.
"The New Testament is reliable because this or that person, or this or that place, really existed."
A very common, and strange, argument that many Christians present, including these apologists, is that since there are some details in the Bible that are demonstrably true, that means that the entire Bible is reliable.
In other word, since it's demonstrably true that this or that king or head of state existed, then that means that the entire story of Jesus' crucifixion and burial is true. This argument makes no sense whatsoever.
You could use the exact same argument to claim that the Harry Potter books are reliable history because they talk about real cities.
"Martyrs wouldn't have died for a lie."
This is an even stranger argument given that people die all the time around the world because of their convictions. Surely these Christians are not going to argue that all belief systems are accurate because of that?
(Of course apologists will respond to this with special pleading, claiming that Christianity is in this regard somehow different from all those other thousands of belief systems.)
"If Jesus didn't rise from the dead, then how did the church begin? You have to give a plausible alternative explanation."(Yes, this really is an argument that some apologists, even very high-profile ones, make.)
I don't even understand this argument. We have countless religion around the world and over all of history. How did they all begin? First a small group of people start believing in something (often the ideas of one single person) and they start gathering more and more people. As time passes, they develop more and more intricate details to their new religion. I don't even see what's the problem here.