I think many answers here are good, but take a different approach than I would. They all presume that spending money to impress girls or fit in is necessarily, and fundamentally, wrong, and there are valid arguments against that. I think the issue to be addressed here is more one of agency.
First, you do not necessarily need your child to not spend money on these things, but you need your child to understand that you will not spend your money on these things. That is establishing your agency. This is what I would call the most important, and most fundamental, financial lesson. That in a capitalistic society agency is often tied to money (whether that's right or not is another question).
He is over a year into adulthood and, unless we are missing information, fully capable of supporting his own basic needs if necessary. Many college students work part (or even full) time to put themselves through school, so your support is not a matter of survival. I think this is important to discuss with your partner. As is the fact that loving someone involves doing what is best for them and not what is most comfortable, though I agree with previous answers that this discussion should be non-confrontational and without blame (or with shared blame). You must both be on the same page or nothing you do will be successful.
Sit your son down together and present a united front at all times. Explain that you are happy to help him with some of his necessities. Lay out what you are currently willing to pay for and establish a budget. In this phase I would recommend that you have a budget of necessities only (rent, tuition, groceries, maybe basic clothing). Explain that he is welcome to spend any money he earns on his own any way he wants. Be supportive and offer to help him every step of the way in finding a job. I especially like an earlier suggestion of offering earnings-match.
During that first phase be explicit about agency. If he is using your money then you get to decide how it is spent. If he is using his money then he gets to decide how it is spent (on anything he wants, without any nagging or negative comments from parents...which is something you must be willing to do). This is an important point. We began using this with our pre-teen daughters and it worked very well to help them see money as a positive thing (something that gives agency) instead of a negative thing (something that limits). Your situation is a little different as your son has already established certain associations with money in the latter sense, but I think this could still help to provide a positive counter-point. Everyone wants control over their own life; help him see this as a way to gain something he doesn't have.
As a second part of this conversation, explain that the amount that you provide to him will decrease by 30% per year (or whatever number you feel is tenable). Explain why you are doing this. He must learn to support himself. You're willing to help by providing assistance as he slowly weans off of your support. Depending on his point of view, and your relationship, you could make a point that any support you give is no longer required of you and is, in fact, a favor. Were my 19 year old to act like any money I gave them was anything other than a treasured gift, they would not receive it, but every parent/child relationship is different. If you want to continue to support him through school, then instead tell him that your support will decrease by 10% per month beginning the third month after he graduates, or something similar. Whatever your plan is, make sure it is clearly communicated so he has expectations and can plan.
Your son will be angry. Your son will likely yell and likely storm off. Prepare for this. Do not show anger; maintain a position of love and support, as if you were forcing a baby to swallow a pill they needed but did not want. If he storms off let him cool down a bit, but in your very next interaction pick up the conversation exactly where you left off. If he asks good questions (as opposed to rhetorical ones out of anger) answer them, but immediately return to the topic. Don't get sidetracked into a tangential point. Most importantly, if he refuses to have the conversation go through with the plan exactly as you would have otherwise. The conversation is not to hammer out an agreement, but rather notification to him of what you have already decided to do. He will come back to get that explanation eventually.
Again, never disagree with your partner during this conversation. The moment you show the slightest crack in that united front he will find a way to drive a chisel in there and pry it into a chasm. It's just what kids are good at.
Feeling guilty, or like you're failing him, or like your bad parents, or like you're putting him in danger are all normal feelings. They will not be comfortable. But you are doing no favors by teaching him to be financially reliant on you for the rest of his life. Uncomfortable as it is, teaching him self-sufficiency is the only real option.
All children are different. All parents are different. All parent/child relationships are different. How you handle this will have serious repercussions both in his life and in your relationship with him. Don't try to follow any advice given in any answer word for word; take it an modify it to fit your situation.
As a parent I know how easy it is to always see our children as our 'little kids'. But he is an adult now and clearly has not yet learned to act like one in terms of finances. This puts him at a disadvantage, and if he is going to compete and succeed in the world he needs to not just start doing as well as his peers, but going above and beyond so that he can catch up.