You have not offered your son anything. Rather, you have made a demand, that if he gets a job in your home town, you demand that he reside in your house.
Regardless of your motivation in making that a demand, it is still a demand, and not an offer.
An offer would be; “if you get a job in OurTown, you are welcome to move back here and stay as long as you want.”
Instead, you are saying, “If you get a job in OurTown, I will raise hell if you choose to rent an apartment for yourself, I expect you to move back home where I will monitor what you eat and your exercise regimen, and freely let you know my opinion of whoever you choose to date.”
If your son is smart he is going to find a job in another city where he can avoid having to confront you.
I hope for your son’s sake that if he does find a job in your hometown, that he has the courage to tell you no. Because there are many potential reasons he might choose to live elsewhere – perhaps an easier commute, perhaps a room or apartment with amenities he prefers, including privacy – and perhaps just the privilege of living somewhere where he doesn’t have to deal with you on a daily basis.
This thread reminds me of a former poster who seemed, as evidenced by his posts, to be very controlling (anyone remember when he unplugged his daughter’s computer just before a scholarship was due and, IIRC, threw it against the wall because she was doing it at the last minute), was very over-focused on $$$ (he claimed never to have any, yet would talk about buying expensive camera equipment, taking all inclusive vacations and having a personal banker). He would argue with posters who suggested he lighten up on his kids, and would talk about turning to alcohol (drinking bourbon and wine, IIRC). At least he didnt comment on womens’ looks, that I recall.
Don’t know from what school the OP’s son is graduating or what he majored in, but it would not be surprising if he wanted to get away and forge his own path. The tone of the OP’s posts sound like conditional love. There are way, way too many strings attached to the “suggestions” to live at home. The OP had talked elsewhere about growing up in a challenging environment, and has forged his own path. He likely has educated his kids on fiscal management throughout their lives. Its time to let the s test his wings. Time to let go. Support the effort, not the outcome. Being controlling and argumentative will not win favors from adult kids. And stop the drinking.