I don't think its unreasonable to ask for half of extra activities. I understand some men just cannot afford it, ok fair enough but the reason of "I don't have to pay for that" bugs me. Of course you don't have to but we are talking about your kids and it would be good for them if they can do things they enjoy.
Growing up yes my parents were together but we missed out on so much as my dad thought if he could pay bills and mortagage that meant the rest could go to himself meanwhile mum had to clothe, pay for school things excursions, pocket money etc on the tiny amount she got from family assistance, so while it is different in a way, I do understand it is dissapointing for a child to not be able to do all these things and have to miss out all the time just because he "doesnt have to pay"