Israel, despite what others may think, is actually rather safe. Statistically speaking, it's safer than most of the US! As such, it should come to no surprise that few Americans are killed over there. Assuming your brother has common sense and knows to avoid the bad neighborhoods that all cities around the world have and dark alleyways late at night, I wouldn't worry too much about him.
A lot of Israel's visitors are American tourists, so the nation isn't a stranger to people like your brother. Most Israelis are actually kind and will be willing to help him if he needs it, provided that he's not a jerk to them beforehand. Furthermore, a lot of Israelis are conversational if not fluent in English, so a huge language barrier isn't to be expected. Many of Israel's signs are also in English, especially street signs, so he's not likely to get lost either.
Now, Israel does come with some precautions....but nothing that should scare away your brother or even your mother. Everyone knows that their neighbors hate them and a few want to kill them...but that's an external threat that the IDF does wonders keeping outside. On the off chance that a war breaks out, his hotel will have some protocol to keep him safe and let him know what it is. If it's an immediate issue, then he should follow the Israelis to the bombshelters, which they'll be able to find quickly. Once again, this is NOT likely to happen but knowing what to do is unfortunately a reality for most Israelis. This goes if he's staying in the North (closer to Lebanon), or close to Gaza, but if he's in Tel Aviv or somewhere more central, or even in the Southern tip of Israel, then the chances of an issue drop significantly. I'll reiterate: Americans expect a very, very low chance of dying in Israel so this is more of a "better safe than sorry" type of message.
Honestly, the areas he'll need to exercise a bit more caution are if he's close to Gaza (for example, in Sderot) or visiting the West Bank. The city of Jerusalem also presents certain issues as well. The Palestinian protests in Gaza have shown the world some nasty contraptions, such as incendiary kites. The area isn't very touristy but if he's does go to this small part of Israel then he should know that he may hear some sort of siren to take cover. Gaza, though, is not an area he's likely to even be able to visit so the most dangerous spot in the area won't be accessible to him. As for the West Bank, it's not always hostile towards Americans but such sentiment is there and the protection of the Israeli police force won't be able to intervene. It's not the worst place to be American, and also not part of what many people consider to be Israel proper (so he may not even go there), but just know that he is increasing his risks if he willingly enters there.
And Jerusalem: There have been terrorist attacks there but the most recent ones are lone-wolf attacks targeting just a few people and honestly haven't happened in a while (or at least none that attracted my attention). In the end, I'd be just as worried as if he were visiting London or Paris, which as of late have had their fair share of attacks yet people still feel safe going there. Jerusalem is tourism central so he just needs to be exercise a bit more caution, but otherwise will be fine. The Israelis have stepped up their game so Jerusalem is once again an overall safe city to be in.
Edit: For Christmas concerns... don't worry, he'll still be safe! If he's going explicitly for religious reasons, then the only thing I'll reiterate is that the same safety levels aren't expected in the Palestinian controlled Bethlehem; but, they generally depend on revenue generated from Christian tourists so I'd trust them as well. I've been in Israel during Christmas, Jerusalem even, and I can say personally that they keep it safe during this time as well. Hell, I think they'll amp up security around the city, making it safer for your brother if he's there.
Fellow American, with extensive experience traveling in Israel