My husband has this habit of doing this- hes done it with me and with the kids, and today with one of our sons, which has upset him a lot. DH will get frustrated by something we're doing/not doing and then say it's fine that he doesn't care and then will come back with a comment that appears threatening and/or criticism. For my 13 year old son, he asked if he could go out with friends instead of to a sports club he does every monday. My husband said yes you can do what you want. So my son thought it was ok for him to go. then my husband came back with 'you need to reassess your commitment to your sports clubs, we pay a lot of money and you always make excuses etc. So then my son was upset as, in his mind his dad was happy for him to go then he changed his mind. I tried to explain to my husband that my son's brain isn't fully developed yet and he doesn't understand the nuances/thoughts beneath the surface that his dad might be having!!
I feel like it's his way of trying to control what he can't ultimately control maybe? I get that our kids have to understand they can't just flunk off a club if they don't feel like it but telling your kid it's 'fine' to miss it but deep down being resentful then telling them we won't be paying for their clubs if they don't go seems to me to be confusing for the child to understand and just causes upset and hurt.
I don't think my husband gets that how he's dealing with it isn't helpful but he won't understand where I'm coming from! He's also a high achiever/very hard on himself so I think he holds everyone to the same level. He never skips a training session even if he's sick.