There are sites like Jews for Judaism and people like Rabbi Tovia Singer and his site (Outreach Judaism) that have plenty of material on this topic.
Ask your LOR what approach to take before you jump into this sewer of engaging missionaries.
As I recall from various sources, off the top of my head:
For starters, the missionary likely does not know a word of Lashon HaKodesh, and therefore anything he quotes you from whatever worthless translation bible he uses is wrong at best and perhaps even fraudulent at worst.
Their own scriptures, too, have many stiros minei ubeih in metzius and elsewhere (not to mention the various conflicting editions), which means the whole thing is certainly not factual and even more so not accurate.
So, their scriptures cannot be relied on to tell anyone that, for example, their savior was born of a virgin (which, not coincidentally, was a popular pagan belief at the time). While on that particular topic, they mis-translate “alma” as virgin.
Understand that as slick and sure of himself as the guy might be, he is more ignorant than most Amei HaAretz and it makes no sense to listen to anything from an ignoramus, even if it might sound like it could make sense.
Even for the better arguments, once you dig a little, the whole thing comes crashing down like the house of cards it (at best) is.
Rabbi Singer’s approach, from what I’ve seen, is to stick to our Tanach, because they, too, liHavdil, also believe in that and, of course, there is not even the slightest support for their faith anywhere in Tanach, of course.
You can try to twist anything to say anything and even fool some people some of the time, unfortunately. But if you’re honest and objective (and educated) then it is clear as day that the Torah does not CH”V allow for Christianity for the Jewish people and, in fact, 1000% forbids it for Jews.