I got the impression that Dean always sided with John and was very gung-ho about the hunting lifestyle until he first started having doubts around late season 1/season 2 time

I assumed that Dean saying he fully embraced the life at 16 is referring to the first time that he went on an actual hunt. John generally left Dean behind to look after Sammy when he went on hunts, so that time with the crossbow was when he first ~became~ a hunter so to speak.