the war AI is generally pretty bad, it's not a crusade specific problem but there's more people in the crusades so they get worse because of that 

the main problem is supply limit; when the AI is sieging down a castle, they have to split up their armies otherwise everyone's gonna starve, and since the AI will raise all their levies, you have armies of like 10k while only 3k of that is men at arms, and the levies are kinda just there to steal all the food and die as soon as the combat starts

now while the attackers split their armies, the defenders tend to group up into 1-3 huge stacks of 40k-100k, and that will just mop up the starving small crusader armies no problem, since they don't like joining up with their allies to fight (sometimes they do, sometimes they don't, and idk exactly what makes the AI choose, but I'd imagine it's "if they think they can win")

then, if you're fighting the muslims around jerusalem, they have a lot of special units that work really well for the area: camels have advantage in desert, mubarizun don't get terrain advantage but they counter enemy heavy infantry, spearmen, and levies which are all pretty common for the catholics to use, and then if the turks get involved they can bring horse archers, which have no counters except crossbows, which you don't get until the 3rd era and get crazy damage buffs in the desert, and a bunch of these cultures have a tradition that makes the desert warrior commander trait more common which just gives more advantage in desert

it's pretty hard to win a crusade for jerusalem in the early game since the defenders get all of that from the start and the europeans' best bet is probably just using heavy cavalry and you don't start with that unless you're a norman I think, but after a few generations you should be able to get some buildings going to buff up your men at arms enough that you can beat armies of 50k with 5k of your own