The crux is, how much time is he
a) attending (and traveling to and from) college?
b) studying independently around that ?
Neither of which you have told us.
Then what time is he taking part in other 'constructive' activities - a sports Team or volunteering, or a music activity or a youth activity?
My dc (Youngest dc, or 3 is now in Yr12) have all had a PT job in 6th form. Have earned enough money to pay for their driving lessons. Not only the ability to drive, but the experience of holding down a job and all the confidence and social skills needed for that have been held in very high esteem when presented with further opportunities later. So I'd agree, in principle with your partner.
Try sitting down and working out how many hours there are in a week, when your ds is awake. Take away eating / washing / dressing / etc. Take away time on jobs round the house. Take away time spent at college + traveling there. Take away time studying at home.
I bet there are still hours upon hours upon hours of time he can then choose to do as he wants with. Yes, including X Box, but I bet there is time for work if he wanted to.
What is his incentive ? Does he not want a phone contract or the latest trainers or to go to a concert or two or to learn to drive ?
As to if your partner should have a say or not - that's going to depend if this is someone who shares your life and your home and is a long term fixture, or a new squeeze you've been dating 6 weeks I'd have thought. I don't think you can rightly live together as a family (if that is what you do) and not expect your partner to have an opinion.