The chicken grinder thing only happens on the aforementioned factory farms. Buy from a local farmer or a small operation, problem solved. In fact, you're actually making things better by encouraging local farmers and taking business away from factories.
Hey - you said you'd never heard any reason why someone shouldn't eat eggs because "chickens are going to lay them anyway". I gave you one. As regards "only happens on factory farms" those are the source of the overwhelming majority of eggs and for a vegan even if it's not, they're going to kill the male chickens one way or another whether it's a grinder (the huge majority of cases) or one by one throwing them over the fence into the organic pig pen next door. It really doesn't make it okay for someone who wants to live without killing animals. You can agree or not but to claim you'd never heard of the reason before makes me think you haven't actually talked to many vegans about this.
The cow one I'm extremely skeptical of. Cows only have to give birth once a year to produce milk all the time, and a calf is far too valuable to slaughter for no reason. They'd be kept for breeding or sold for meat. I've never heard of this "technique" before, and the only information I can find online about it comes from a small handful of PETA-grade lunatics. And even if it does happen, once again, buy small, buy local, problem solved.
Who said it would be slaughtered "for no reason". The meat then gets sold. It's not "a technique" you've never heard of, it's basic facts - you can't milk a bull (at least, it wont be the sort of milk you want!). Ergo, male calves are disposed of. It makes little economic sense to provide all that resource to raise a bull you don't need when you could put the same energy into raising a cow that can provide you a few milk giving cycles and then still be slaughtered for meat later on. You're trying to shift ground with things like "only give birth once a year" to some sort of 'it doesn't matter if I'm wrong, I'm still right' sort of position. Think through the basic logic - there's only a certain amount of milk the market needs. If in year 1 it's met by X cows and you get three cycles out each cow, then why and how would you be raising each of the calves of these cows - by year 4 as you're retiring the original cows you now have 3x the number of dairy cows than the market actually wants. I mean, I'm simplifying but of course the extra cows are killed. Meaning that vegans don't want to drink milk because it's resulting from a process that requires killing animals.
You were ignorant. That's not a crime. You don't have to agree with the vegans about the importance of animal life. But saying bollocks like you've never heard a vegan give a reason for this sort of stuff and then when you're provided one trying to pretend the reason doesn't exist rather than just saying you don't care about it. Well, it makes you sound stupid, you know?