This is not the same question as the one mentioned in the comment by Martin Sleziak, and your "correct ans" is wrong; the probability (under the assumption, not quite true in reality but reasonable for this question, that the probability of a random person being male $\frac12$, and that it is independent of the gender of any other fixed person) is indeed $\frac12$.
The question is equivalent to the following one: you pick a random person $p$ and ask what are his siblings; it turns out $p$ has just one brother. What is the probability that $p$ is male? You could also say, "pick a random man $m$ with one sibling, what is the chance that his sibling is a brother" (which more closely resembles the setup of your question); it is just another equally random way to make the selection (take $m$ to be the brother of $p$).
There are all kinds of ways to see the answer is $\frac12$ here, basically because the gender of one sibling is independent of the other. If you like detail: there are $4$ possibilities for genders in $2$-child families, in oldest-youngest order $FF,FM,MF,MM$, all equally likely. Person $p$ could be oldest or youngest, treat the cases separately (they give equal probabilities in the end anyway). Supposing $p$ is oldest, the fact that the younger sibling is a brother eliminates two possibilities leaving $FM$ and $MM$; this leaves equal probabilities for $p$ being female or male. If $p$ is youngest, then $MF$ and $MM$ are left, again leaving equal probabilities for $p$ being female or male.
The essential point that distinguishes this question from the one linked to is that you are not given that "one of the siblings is a boy", which gives a different kind of information (eliminating only one of four possibilities). Here a specific sibling is found to be a boy.