A time-tested piece of utopian thinking, with (as with most utopian thinking) one major flaw:
Start from the idea that most of the problems in the world today ultimately boil down to people. People are vain, foolish, easily led, easily duped; thus, all manner of political and practical problems. I'll agree that this is probably not an unreasonable starting point.
From there, the obvious next step is to conclude that we should make the next generation better somehow. Eugenically, through genetic manipulation, through euthenics and cultural indoctrination, whatever. Again, a not unreasonable solution to a clear problem.
However - and this is a big however - you have to do that with the resources you have today. That is, some person or people, currently living, must be the judge not only of what actual, direct actions will make the next generation "better", but what constitutes "better" in the first place. Given that, per our very basis for this line of thinking, people today are flawed, how do we know who to pick? If there are no "better" individuals in society, obviously no one individual's plan is likely to be better than the aggregate's plan. If there aren't - and I wouldn't say that nobody is better than anybody else, this isn't Harrison Bergeron - we have to find those better people... so that they can pick the better people.
I'm sure you can see how this is going to go. We can't find the better future people because we need better people to do it. We can't find the better people to find the better future people because...
So ultimately, we either stick with what we have, or we put our faith in our collective ability to pick somebody less stupid than us for the purpose of making us less stupid, because our (stupid) inability to pick non-stupid people to lead us is causing problems.
TL;DR: From a practical perspective, the reason to avoid a controlled breeding scheme is that it's impossible to decide objectively whether it will actually help anything or not.