I would like to know why the urine of a girl is consider as "dirty" (i.e. one can't pray with it on the clothes) and that of a boy is not?

All perfect praise be to Allah, The Lord of the Worlds. I testify that there is none worthy of worship except Allah, and that Muhammad is His slave and Messenger.

Know that there is no difference between the urine of a male baby and female baby as far as the ruling of impurity is concerned; both are impure according to the view of the majority of the Muslim scholars.

The difference is only in the way of cleaning that urine. It is sufficient just to sprinkle water over the urine of an unweaned male baby. But the urine of a female baby should be washed off completely. This ruling is based on the Hadeeth that an unweaned child who has not yet begun to eat, was brought to the Prophet . The Prophet put him in his lap, and after a while the baby urinated in his lap. Then the Prophet . called for some water, which he sprinkled over his clothes, and did not wash them completely. [Al-Bukhari and Muslim]

The Prophet also said: “The urine of a baby boy should have water sprinkled upon it. The urine of a baby girl is to be washed off.” [Abu Dawood, An-Nasaa-i and Ibn Majah]

The Muslim scholars pointed out many reasons for the easiness concerning the ruling of cleaning the urine of a male baby.

First, the urine of a baby boy usually does not fall in one place; rather, it spreads widely, and washing it frequently causes much hardship unlike the urine of a baby girl. So, the ruling of cleaning is different from male baby to female baby.

Second, the urine of a female even when she is baby is more noxious and foul smelling than the urine of a male. Because the temperature of the body of a male is hotter than the temperature of a female's body and no doubt that the temperature decreases the bad smell.

Allah knows best.