Okay I'm new to the forums, but this particular subject is one I've done a lot of my research/studying about. While it's true boys tend to have less empathy, a lot of people feel it's more a function of how boys are raised than anything. My father (though I love him dearly) has very little empathy. He often laughs at other people's problems because they're not things that would necessarily bother him. He was raised in a completely different era where he was punished for trying to show his feelings. While we are in a different society now, there are still many children, but especially boys, who are encouraged (sometimes very strongly) not to cry, that it's wrong to be upset, etc. Empathy starts with the parents modelling it, by having empathy towards the child when the child is upset about things, even when they are things that the parent wouldn't be upset about. Modelling understanding and compassion towards children will help them learn to develop those skills. I recently read a study about empathy and compassion in kindergarten-age children and the different parenting that was pretty interesting. Also, kids who are punished for things without being given any information about what they could do instead and how to be gentle, are just going to resort back to that behaviour when there's no one around to watch.
That being said, some kids develop empathy early, and some develop it late (some studies have shown that the receptors in the brain that control empathy often don't mature fully until adulthood). I'm not necessarily trying to blame the parents, since I obviously don't know them. He could just be really late developing it, or he could just be that way despite the parent's best efforts. You can teach a kid to be gentle with animals, but you can't really teach them empathy, only model it and encourage it's development. We got a kitten last year when my daughter was 2 1/2. She was terrible to the kitten at first. We had to be there on top of her literally every second. But we pointed out to her the signs that the kitten was not happy, talked about why he might not like something, etc. Luckily, that kitten still adores her to this day. They spend every morning curled up together on the couch while she wakes up. She is fantastic with animals now and is really good at looking for signs that the animal is upset. I don't know if I could say she's developed empathy, but she is at least aware that others have signs they're not happy. She's only 3 1/2, and you know, I have left her alone for brief times with a chick. It's not something I would do on purpose or for long lengths of time, and not with a day old who she could hurt by accident very easily, but with a 3 or 6 or 9 week old chick? I've done it. Mostly if I've had to run after our one year old or to run to the fridge to grab the meal worms, not like I would get a chick out and then go take a bath or something. But I would be shocked if she purposely dropped a chick a couple of feet, let alone throwing it up in the air.
Anyway, all that to say, I don't think this can be blamed on "boys will be boys". I know some pretty compassionate and gentle boys and men, and I know some pretty unempathetic little girls (and women). I don't have a six year old, but I would think if my 3 year old knows that throwing an animal is not okay, a 6 year old should know it too. Do you know, did he seem to feel bad? And I mean, genuinely feel bad, not just for show because he thought he was supposed to. If he seemed to genuinely feel bad about it, I personally probably would have him back, but with very very careful supervision and teach him how to properly handle and care for the birds. Maybe his "punishment" could even be coming over to help you care for them (scoop out the litter, change the feed, etc) while you talk about how they grow, their feathers coming in, etc. Might do him some good. If he just thought it was funny and didn't seem bothered by the incident at all, I would think twice about having him back though.
Anyway, my opinion may not be wildly popular.
I'm definitely of the opinion that more and harsher punishments don't do our kids any good. But I thought I'd throw my two cents in here. I'm glad your chick is okay. I used to work at a vet clinic, and though I don't know much about chicks specifically, I would say if she's eating and drinking as normal, and doesn't seem to be in any pain when picked up, keep an eye on her poop for blood but she's probably fine.