Part of the reason comes from politics. The original crusades were supported by several Catholic states who worked together to combine their military strength. There are very few Catholic states today. Malta is still officially Catholic. Most of the countries in Latin Americas come to mind, but there’s a difference there: I think they have majority Catholic population, but don’t have official state churches, and I don’t think their leaders take their faith seriously enough to attempt a crusade.
In order to have a crusade, you can’t just send out a request for a bunch of people to go to Israel and fight. There has to be military training and an authorized leader. The original crusades were primarily a call for knights to go to war and their countries to support them. Commanders were worked out on an international level. If we did something similar today we would have to primarily call for trained soldiers to go to war. We could ask the countries of origin to support them, which would help. But it is my guess that no countries would answer the call, maybe only one or two, and, perhaps worse, most soldiers wouldn’t be allowed to leave their period of service to go on an unauthorized mission.
The pope has spoken out in favor of military action against ISIS:
“With terrorism one must fight, but I repeat what I said in my previous trip: when an unjust aggressor must be stopped, it must be done with an international consensus.” source
“One nation alone cannot determine how to stop an unjust aggressor. … To stop an unjust aggressor is a right of humanity, but it is also a right of the aggressor to be stopped in order not to do evil.” source
“In reaffirming that it is licit, while always respecting international law, to stop an unjust aggressor, I wish to reiterate, moreover, that the problem cannot be resolved solely through a military response.” source
That is similar to what the crusade popes did. They said it was legitimate for an international military to go to stop the Muslims. That’s what Pope Francis says too. The popes then said we Must do this. So has Pope Francis. In historical context, Pope Francis’s call was in the midst of a coordinated effort by several countries to stop Isis, including the USA, France, and Australia. (Russia recently started to help too.) In the original crusade period too, France, Italy, and Germany went in to fight. To me, this too is similar.
In those days, the pope himself spoke about the sufferings of the christians who lived in areas conquered by the muslims & publicly declared that it was legitimate & even praiseworthy for christians to try to reconquer those territories. … So why is it that the Pope of today doesn’t act as the popes of previous times did? I understand norms change, but is the justification which existed back then different today?
In my view, what the pope is doing today is very similar to what the popes did back then. A big difference is that he has to deal with secular governments rather than Catholic ones. The pope has talked several times about the legitimacy of fighting ISIS, and has even said we “must” do this. (See the quotes above.) But he can’t organize a Catholic army to do this, because there are very few Catholic states and modern military authorities aren’t willing to release a big chunk of their soldiers to form a Catholic army. Instead, the pope is supporting efforts by international non-Catholic nations to go in and fight ISIS, while reminding them to follow the principles of just war.
You may also be interested in the group Sons of Liberty International. They are a group that provides military training for people who want to fight ISIS. They were founded by a gentleman who earned his degree in Middle Eastern Security Studies from Georgetown University, which is Catholic (at least in name). I’ve helped donate some money to them and they provide regular updates about their training programs in the middle east and their military successes. Here’s their website. They are currently training two groups to fight ISIS on a volunteer basis: Dwekh Nawsha and the NPU (the latter appears to be more explicitly Christian and Catholic).
I hope that helps. Please let me know if it does. God bless!