There must have been 1 more boy than girl in the family.

This is because once we select one boy (to count the remaining children), we realise that the remaining number of boys and girls are equal.

Now, we take it a fact that there is one more boy than girl in the family.

By similar logic, once we select one girl instead (to count the remaining children), we realise that amongst the remaining children, there would be two more boys than girls.

But this "two more boys and girls" would be the reason why there are half as many sisters as brothers.

So, if we let the "remaining girls" be 1 unit, then the number of boys will be 2 units.

The difference of 1 unit will be the "two more boys than girls".

1 unit = 2 people
2 units = 4 people

Including the one girl chosen, there are 3 girls and 4 boys in the family.