Conditional Probability - 2 Bears

I may be bad at applied sciences but I know I damn good at pure sciences - especially math - especially probability. Therefore one probability problem that I keep encountering is that of 2 bears where the answer given by the problem creator is always the same and is always wrong! I therefore feel so strongly right about my answer that I will put it forth in this blog and wait for the reader's comments.

Problem:
There are 2 bears - one black and one white. One of them is male. What is the probability that both of them are male?

My Solution:
This is a problem of conditional probability. The condition is given, that one of them is male. Now the question is, is the other one also male? The probability that the other one is male is 1/2. Also, if the other one is male, then both are male, then the probability of both being male is also 1/2.

The so-called Expert's Solution: (copy-pasted from a site)
"Now assume I told you that one of the bears is male. What is the probability that both are males? Of the three possible outcomes (mf, fm, mm) only the last where both bears are male is favorable. The answer is 1/3."
Isn't the error glaring at your face? If you are so sure about one of them being male, then why include him in the sample space? It does not matter whether the white one or the black one is the male. The sample space should only be (m,f). By giving the answer as 1/3 you are implying that there is a 2/3 chance that the other bear is a female.

These buggers go on to add that if it is mentioned that the white bear is male, then the probability of both being male becomes 1/2 (my answer). I repeat, it does not matter which coloured bear is male. Now I know what troubled Michael Jackson enough to write the song "It don't matter if you're black or white." It wasn't bigotry and racism, it was this confounded problem.

I've seen such answers all over the web and do not understand how so many people could be wrong in the same or similar problems! Comments are welcome!