From a purely logical standpoint it doesn't make sense, but then we are not wired to be purely logical.
Dead is of course dead, and death due to dogs, lightning or pencils is probably pretty unpleasant, but very few people have fear of dying from such encounters, unless they are actually faced with them (well, may be not with pencils).
I'm sure someone like Steven Pinker can explain it far better than I can, but it is the case, and simply insisting that people stop thinking that way isn't going to be of any help.
I would go so far as to suggest that when the people who the public rely on to protect them insist that they have little or nothing to worry about, it pisses off a lot more people than it mollifies. Part of it is trust in these people. If you don't trust someone responsible for protecting you, you're not likely to welcome them telling you not to worry. When stories appear in the news about the government refusing to allow reviews of the FB pages of Visa applicants, it erodes trust.
Obviously this is not to say that people should be encouraged to panic or that efforts to point out the low probability of anyone dying from a terrorist are not appropriate. (If I had small children now, I would be doing so with them). However, I don't think Americans are only concerned about their personal safety and that of their loved ones when it comes to terrorism. Ultimately, it's at those levels that the rubber meets the road but I would not deny or dismiss the outrage and grief that Americans thousands of miles away feel when terrorists gun down innocent fellow Americans. It's much more than fear.
Recently President Obama, I guess in an attempt to reassure Americans, made that the statement that ISIS can't destroy America. Putting aside what terrorists with a nuclear bomb can do, I don't think anyone believes ISIS can destroy America so it's not very helpful to tell them something they already know about a risk they weren't fearing.
There are ways to deal with people's fears (rational or otherwise) and while I'm not certain of the best way to address fear of terrorism, I have a pretty good idea of what doesn't work.
What's not helpful at all is to ask people to take risks that are not warranted. Those in favor of allowing 10,000 Syrian refugees into this country need to explain why the risk is warranted. Denying there is a risk is foolish and insulting and even more insulting is to suggest to someone who is not inclined to take the risk that their unwillingness is born of xenophobia and irrational fear. It would be irrational to assume all 10,000 of the refugees were agents of ISIS, it is not irrational to assume that some of them are. If only 10 refugees are ISIS agents and only 1 of them is successful in killing 14 Americans and wounding 17 (as was the case in San Bernadino) then someone will need to explain why the lives of 31 Americans was worth bringing in 10,000 refugees. Before we allow them in I would like to hear proponents explain why even one American death would be worth it.
The answer that we need to take these people in because it someone sends a message to ISIS or is an effective means to combat them is not, at all, compelling. The answer that we need to take the risk because the alternative is not acceptable to our values is not compelling either because the alternative is not surrendering them to the tender mercies of ISIS, or even dooming them to live in squalid refugee camps in Jordan.
As I stated previously I am all for helping these people. Thus far I don't think we've helped them enough. I just don't think the only way, or even the best way, to help them is to bring them into this country. The issue needs to be discussed without assumptions of negative intent, and without dismissing out of hand the concerns of millions of Americans.