Trade a bishop in the opening In several openings white or black trades a bishop for a knight (Ruy Lopes exhange, Sicilian Rossomilo, Nimzo Indian etc).

I have learned the bishop pair is worth a half pawn, and I have difficult to understand these trades, which to me look bad. The opponents pawn structure get worse, but is this enough compensation for the trade?
In general there are two scenarios in the opening where one side might want to exchange one of their bishops for a knight.


The knight controls key squares in the center which are being
contested. In the Nimzo, for instance, the knight on c3 controls e4.
White would really like to put a pawn there. Pinning and then
exchanging that knight makes the e4 pawn push far less likely. 
Similarly in the Dutch black sometimes plays Bb4 to pin the knight on c3 to weaken white's control of e4 and will swap if a3 or O-O is played.
Where one side has control of most of the space on the board that normally gives them an advantage because they have more room to manoeuvre their pieces and can switch the point of attack more easily. The side with less space, conversely, often struggles. However there is balance between space and number of pieces. More space with lots of pieces confers an advantage. Reduce the number of pieces and the pawns defending that space become overextended as the few remaining pieces struggle to defend them. Similarly a cramped space with lots of pieces becomes a comfortable one when pieces are exchanged. So, again, in those positions it is often worth one side exchanging a bishop for a knight.