It begins with a GM casually mentioning that the DH campaign seems to have the momentum of a runaway freight train. Why is it so popular, the little girl asks? And then it moves from casual mention to actual news when it gets closer to Collective Bargaining Agreement time. Then there are 1,000 different articles and think pieces and haiku about the DH as the debate rages among anyone who isn't actually involved in the decision. Then the decision is made, and there's nothing you can do about it.
Then you get used to it.
That's how it will happen. Trust me, I'm not looking forward to the DH, either. I'm a huge supporter of pitchers hitting for the same reason most people are: I'm used to it. If you're a proponent of designated hitters, you're probably extremely partial to them for the same reason most people are: You're used to it. And eventually, no matter what happens, you'll get used to the DH in both leagues, or you'll get used to pitchers hitting in both leagues.