In the context of the post, 17 year olds are incapable of 'Having and fulfilling adult responsibilities' while 18s fully can, which doesn't make sense biologically, therefore putting arbitrary age restrictions doesn't make sense.

You become an adult when you become an adult and your psyche will be able to deal with things when it becomes able, not when you live for 6570 days (18 years) or whatever.

We don't have evidence that that specific - and imaginary - 13 year old isn't, maybe he isn't fully ready, but he's ready enough to deal with what he has to deal with. (remember people don't go from being treated like kids to having a 9 to 5, I am not saying we should let him bear his responsibility fully, but I think many 13 year olds, depending on how they're raised and genetics and climate and other factors, can have a part time job - at least, and do have the spirit of an adult, if not the the full set of abilities)

Also it is for the better to keep everyone close to using most of their abilities, abundant free time will lead to psychological issues most of the time, burying your worries in work is mostly healthy and increases the quality of life.

(That obviously dependents on WHAT you're burying, but work is probably the cure)

(Also I am not saying we should kick 13 year olds from school and encourage them to get jobs instead of education)