A husband doesn’t have to give a divorce (Get) if he doesn’t want to if he wants to remain married to his wife. Even if she wants a divorce. That’s the rule and law in the Torah and as codified as Halacha in Shulchan Aruch.
There are a very small number of exceptions where she’s entitled to a Get upon request, when the situation meets one of the few exceptions specifically listed by Chazal stating so. But as Avira pointed out even in those exceptional cases he’s not obligated to give a Get unless and until a bona fide Beis Din that both parties agreed to its jurisdiction over their case rules he’s obligated, after conducting a full Beis Din trial and reaching a Psak Halacha whether an obligation exists or not.