My DH is Muslim and I'm not. Have been reading a lot about this in particular as we are expecting a DS. I've noticed a lot of people aren't sure on why it's done.
There are a few reasons behind why Muslims circumcise and I may well miss some but the main points are that it does say in the Quran to follow Ibrahim's example who was circumcised. In Hadiths (which are attested accounts of the life of Mohammed ie the perfect Muslim so hadiths are a kind of guidance document) say that it is one of the five fitra or ways to keep clean, consider that Muslims pray five times a day and they have to clean themselves before prayer every time, if you're uncircumcised you have to wash your privates as well. Mohammed also circumcised his grandsons as another example.
There is a lot of supposed science behind the benefits and disbenefits of circumcision both for and against.
As a Muslim you are obligated by the Quran to raise your children Muslim hence why this is done at such an early age, it's also to avoid more pain/memories when older. On judgement day you're actions will be assessed, as a parent did you do everything you could to support your children to be Muslim? If not then you won't be entering heaven.
@Bluelady I'm sorry for the reactions you've had on here. I do think that this would be used as another way for people to remove others they don't want to be in the country. Cause and effect, you can't say that by making circumcision illegal you won't force Jewish and Muslim people to leave or take the practice to unlicensed practitioners because it will as they are otherwise unable to perform a religious duty required of them.