We will assume all the obvious implicit assumptions (eg. random child being boy of girl is 50/50, boys and girls open the door uniformly, etc.).
If you had a slightly different question, i.e. if you asked the couple if they have at least one boy, and the answer is yes, then the chance of the other one being a girl is 2/3. Intuitively, the probability is not 1/2 because in this case the answer depends on both the children, i.e. it is a function of both of them considered together.
However, if you asked the couple to pick a child at random, then she/he bears no information about the other child, and consequently his/her gender does not give you any information about the sibling.
Your case is the second case, where the child opening the door is selected at random, and she happens to be female. This does not bear any information regarding the other child.
So answer is 1/2 and your friend is correct.
Mathematically,
$P(Other\ is\ B|G\ opens\ door) = P(BG|G\ opens\ door) =$ $\frac{P(BG\ and\ G\ opens)}{P(GG\ and\ G\ opens\ door) + P(BG\ and\ G\ opens\ door)} = \frac{1/2*1/2}{1/4+1/2*1/2} = 1/2$
(Note here, that $P(BG\ and\ G\ opens)=P(G\ opens|BG)*P(BG)=1/2*1/2$.)
However as a digression, a twist in the question can be brought about - if you take probabilities for a boy and girl to be different for opening the door.
Eg. suppose boy opens with probability $p$, girl with $q=1-p$, in a family with BG.
Then $P(Other\ is\ B|G\ opened\ door) = P(BG)/P(G\ opened\ door) = $
$\frac{P(BG\ and\ G\ opens)}{P(GG\ and\ G\ opens\ door) + P(BG\ and\ G\ opens\ door)} = \frac{1/2*q }{1/4+1/2*q} = \frac{2q}{2q+1}$.
This means $q = 0 \implies P(BG|G\ opens)=0$. That makes sense, since girls don't open the door if there is a boy, so definitely the other one is girl too.