How can I deal with defenses I don't like? I like to play 1. e4, as I favor open and dynamic positions, and feel comfortable with most black responses, but I there are some openings I don't like, e.g. Sicilian or French. My aversion might be unreasonable, but I would like to know how to deal with this situation psychologically. Should I play e.g. 1. d4 instead in order to avoid these responses at all? Should I study these openings and try to overcome my aversion? Should I voluntarily use "drawish" lines like the exchange variation in French? Should I play unusual lines in order to throw the opponent out of the book (e.g. f4 in both openings)?
No matter what your first move will be, you will always run the risk to encounter some openings you don't like. It's the same with endgames. At example, I do hate mating with bishop and knight, but I had to do it once to win the game. Should I have avoided that endgame or agreed to an early draw instead, just because I don't like it (and because I forget half the time how to win this bloody endgame)? Avoidance is no option, sometimes you just have to endure unpleasantness. Never throw away a game by drawing early only because you don't like the opening.

Secondly, don't play something to "punish" your opponents because they played something you didn't like. Your opponents will always try to play something which is unpleasant to you, like attacking your king and mating you ;) If you like the exchange variation of the French, then by all means play it. But if you play it just to annoy your opponent ("hah, that will teach you to play the French ever again..."), think twice. You are playing to win the game, not to eradicate the love for the French opening in the world! Only ever choose a line because it suits your goal (like getting a good position, winning/drawing the game etc.).

My suggestion is to look into the reasons of your aversion. Don't you like the resulting positions? Ask yourself why. Is it because you don't understand them or because your play is not as good in them as in other positions? Then you found a spot worth of improvement! Is it because you don't like the kind of play resulting from such positions (like too many or too few open lines, etc)? Nearly every opening offers lines to steer the game into different kind of waters. Have a look at some games of your unpleasant openings, pick the ones you would have enjoyed most to have played and then look deeper into the lines/systems that the White player employed there. In the long run, you need to hone your skills even in areas you are not interested in. For some people it's those boring closed positions, the next one can't stand pawn endgames, etc., but to become better, you have to master those situations as well. And as soon as you do, you will begin to like those situations. So this is the way to go to avoid unpleasant situations: Make them pleasant to you because you can handle them.

That said, I must say that if you are really unhappy with the openings your play produces, changing your opening repertoire might be a terrible good idea, indeed. Just don't expect you can avoid playing unwanted openings that way. Every opening move can lead to openings you don't like.