There are many, many things to talk about here, so this is only a very brief list of what the video got wrong.
- 'Muslims attacked Christians for hundreds of years', which also features the obligatory terrible map provided by 'Dr Bill Warner', which I discussed in some detail here and here. The map is incredibly unreliable because it cherry-picked battles to show Muslim expansionism, but the biggest problem is that it characterised every battle fought by Muslims as a 'Muslim' battle. If we follow the same standard for Christians, then there would be a lot more 'crusade battles' too... Furthermore, as /u/cptbuck has discovered, the 'source' for the map is this appalling dataset, which speaks for itself really.
- Frankly, the more important point is so what if various Muslim polities invaded various Christian kingdoms - they were all different people and led by different individuals. There is no absolutely no reason to group them together, certainly not the alleged overriding agenda that caused them to want to destroy Christianity. Throughout the middle ages, Muslims were just as liable to be fighting their Muslim neighbours as people of different faiths. We should always look at the entire context of each conflict, not to reduce them to a single cause and a single overriding agenda. People and their actions are incredibly complicarted, so we should never view the past as though everyone had a single motivation.
- 'Sheer brutality from Islam'. I fail to see how Muslim armies behaved any differently from any other forces of this period. For example, Sassanian Persians brutally sacked Jerusalem in 614 and carried off thousands of captives and the True Cross back home, whilst the Christian emperor Heraclius specifically burned fire temples when he invaded Persia in the late 620s. Churches and monasteries were generally pretty reliable sources of loot (just ask the Vikings), so raiders targeting them is understandable, if still abhorrent to us today. As for 'brutal' Muslim practices and their subjects, well, minorities probably prospered better under Muslim rule than under Christian rule, with the treatment of Jews being the best example. This does not justify any discriminatory policies in the past, of which there were many, but it is rather hypocritical to point out how badly minorities were treated under Muslim rule without also noting how cultural, religious, or socio-economic others/minorities were generally treated horribly by the 'majority' throughout history.
- I'm unfortunately not qualified to talk about the Arab slave trade.
- Here's the 'main' point, that the Crusades were a justifiable response to the conquest of the Holy Land by Arab forces in the seventh century. Yeah... the Arab conquest of Jerusalem was by all account relatively bloodless, as the patriarch of Jerusalem negotiated a deal with the besieging force, whilst the conquest of Jerusalem by the Crusaders allegedly led to rivers of blood flowing through the city. Of course, these two events cannot be compared, but it is nonetheless ludicrous to say that Christians took back Jerusalem - the Arabs took it from the Eastern Roman Empire. There was no sense of Christian solidarity back then, certainly not the sort that the loss of Eastern Roman territories would lead to western Europeans fighting to regain territories for the emperor of Constantinople. The Romans were involved in instigating the First Crusade, but they simply wanted a force of western knights to back them up against Constantinople's enemies (mostly the Turks), not to return the Holy Land to Roman control. As we know from later events, the Crusaders were not keen to serve under the emperor either.
- The video makes a strange point about how the Crusaders' massacre of the population of Jerusalem was somehow acceptable... in that case, so were whatever Muslim atrocities committed in the name of Islam then. Strange how Christian atrocities were justified but Muslim ones weren't. Hmmm....
- ''The Crusades were necessary'. Why, why must there be a 'cultural' response to the Muslim world? The video simply does not justify this.
- The video then jumps into the Armenian genocide, which is again another topic I am not qualified to talk about. But as before, other factors were involved. I hear that nationalism was a pretty big thing in the modern era, for example.
- 'The Christians were getting more civilised before they had to get down into the dirt to deal with Islam' - well, how about some examples of why they were 'more civilised'? I suspect that our specialists here on the high medieval period can write A LOT on this. This point sums up much of this video: a lot of assertions, but very little evidence - what evidence it does offer is not grounded in modern scholarly analysis, but instead in polemical and bigoted sources that serve an ideological agenda.
I have elsewhere written quite a bit about the rise of Islam, for example here on why the Arab conquests succeeded and Christian reactions to them. /u/thejukeboxhero has also written an excellent answer who what caused the First Crusade here, likewise for /u/Valkine here. Between these answers you should get a decent idea of the main issues involved, but please do let us know if you have any follow-up questions!