That was never the stated aim and not even in the list of aims. The aim of the Crusades -- especially the first -- was to free Christian lands. And Jerusalem etc. WERE still Christian, heavily.
If it was "kill the infidel", the Crusaders would have aimed for Mecca after conquering Jerusalem.
it's a pity they didn't
It would be interesting to know to what extent the kid was using irony.
Jerusalem had been ruled by Muslims for over 450 years. It was primarily inhabited by Muslims at this point.
I agree that the Crusades were at base a long-delayed counterattack, but it is just silly to claim they were intended to rescue the Christian inhabitants of Jerusalem.
Here’s an account of the capture of the city, as written by one of the Crusaders. This particular guy does seem to think killing infidels is a great thing.
The pillage of Jerusalem
Now that our men had possession of the walls and towers, wonderful sights were to be seen. Some of our men (and this was merciful) cut off the heads of their enemies; others shot them with arrows, so that they fell from the towers; others tortured them longer by casting them into the flames. Piles of heads, hands and feet were to be seen in the streets of the city. It was necessary to pick one’s way over the bodies of men and horses. But these were small matters compared with what happened in the Temple of Solomon, a place where religious services are normally chanted. What happened there? If I tell the truth, you would not believe it. Suffice to say that, in the Temple and Porch of Solomon, men rode in blood up to their knees and bridle reins. Indeed, it was a just and splendid judgement of God that this place should be filled with the blood of the unbelievers, since it had suffered so long from their blasphemies. The city was filled with corpses and blood.
From Raymond d’Aguilers, Historia francorum qui ceprint Jerusalem